How to find the perimeter of a rectangle - SSAT Upper Level Quantitative

Card 0 of 28

Question

The length and width of a rectangle are and . Give its perimeter in terms of .

Answer

A rectangle has perimeter , the length and the width. Substitute and in the perimeter formula, and simplify.

$= 2 \left ( x+16\right ) + 2 \left ( 2x-7\right )$

$= 2 \cdot x+2 \cdot 16 +2 \cdot 2x-2 \cdot 7$

Compare your answer with the correct one above

Question

A rectangle has length 30 inches and width 25 inches. Which of the following is true about its perimeter?

Answer

In inches, the perimeter of the rectangle can be calculated by substituting in the following formula:

$P = 2 (30 + 25) = 2\times 55 = 110$

The perimeter is 110 inches.

Now divide by 12 to convert to feet:

$110 \div 12 = 9 \textrm{ R }2$

This makes the perimeter 9 feet 2 inches, which is between 9 feet and 10 feet.

Compare your answer with the correct one above

Question

The length and width of a rectangle are and , respectively. Give its perimeter in terms of .

Answer

The perimeter of a rectangle is , where is the length and is the width of the rectangle. In order to find the perimeter we can substitute the and in the perimeter formula:

Compare your answer with the correct one above

Question

The length of a rectangle is and the width of this rectangle is meters shorter than its length. Give its perimeter in terms of .

Answer

The length of the rectangle is known, so we can find the width in terms of :

The perimeter of a rectangle is , where is the length and is the width of the rectangle.

In order to find the perimeter we can substitute the and in the perimeter formula:

Compare your answer with the correct one above

Question

A rectangle has a length of inches and a width of inches. Which of the following is true about the rectangle perimeter if ?

Answer

Substitute to get and :

$W=5t=5\times 4=20$

The perimeter of a rectangle is , where is the length and is the width of the rectangle. So we have:

$P=2L+2W=2\times 25+2\times20=50+40=90$ inches

Now we should divide the perimeter by 12 in order to convert to feet:

$Perimeter=90\div 12=7.5$ feet

So the perimeter is 7 feet and 6 inches, which is between 7 and 8 feet.

Compare your answer with the correct one above

Question

Perimeter of a rectangle is 36 inches. If the width of the rectangle is 3 inches less than its length, give the length and width of the rectangle.

Answer

Let:

$Length=x\Rightarrow Width=x-3$

The perimeter of a rectangle is , where is the length and is the width of the rectangle. The perimeter is known so we can set up an equation in terms of and solve it:

$\Rightarrow2x+2x-6=36$

$\Rightarrow 4x-6=36$

$\Rightarrow 4x=42$

$\Rightarrow x=10.5$

So we can get:

inches

inches

Compare your answer with the correct one above

Question

Which of these polygons has the same perimeter as a rectangle with length 55 inches and width 15 inches?

Answer

The perimeter of a rectangle is twice the sum of its length and its width; a rectangle with dimensions 55 inches and 15 inches has perimeter

inches.

All of the polygons in the choices are regular - that is, all have congruent sides - and all have sidelength two feet, or 24 inches, so we divide 140 by 24 to determine how many sides such a polygon would need to have a perimeter equal to the rectangle. However,

$140 \div 24 = 5 \frac{5}{6}$ ,

so there cannot be a regular polygon with these characteristics. All of the choices fail, so the correct response is that none are correct.

Compare your answer with the correct one above

Question

The length and width of a rectangle are and . Give its perimeter in terms of .

Answer

A rectangle has perimeter , the length and the width. Substitute and in the perimeter formula, and simplify.

$= 2 \left ( x+16\right ) + 2 \left ( 2x-7\right )$

$= 2 \cdot x+2 \cdot 16 +2 \cdot 2x-2 \cdot 7$

Compare your answer with the correct one above

Question

A rectangle has length 30 inches and width 25 inches. Which of the following is true about its perimeter?

Answer

In inches, the perimeter of the rectangle can be calculated by substituting in the following formula:

$P = 2 (30 + 25) = 2\times 55 = 110$

The perimeter is 110 inches.

Now divide by 12 to convert to feet:

$110 \div 12 = 9 \textrm{ R }2$

This makes the perimeter 9 feet 2 inches, which is between 9 feet and 10 feet.

Compare your answer with the correct one above

Question

The length and width of a rectangle are and , respectively. Give its perimeter in terms of .

Answer

The perimeter of a rectangle is , where is the length and is the width of the rectangle. In order to find the perimeter we can substitute the and in the perimeter formula:

Compare your answer with the correct one above

Question

The length of a rectangle is and the width of this rectangle is meters shorter than its length. Give its perimeter in terms of .

Answer

The length of the rectangle is known, so we can find the width in terms of :

The perimeter of a rectangle is , where is the length and is the width of the rectangle.

In order to find the perimeter we can substitute the and in the perimeter formula:

Compare your answer with the correct one above

Question

A rectangle has a length of inches and a width of inches. Which of the following is true about the rectangle perimeter if ?

Answer

Substitute to get and :

$W=5t=5\times 4=20$

The perimeter of a rectangle is , where is the length and is the width of the rectangle. So we have:

$P=2L+2W=2\times 25+2\times20=50+40=90$ inches

Now we should divide the perimeter by 12 in order to convert to feet:

$Perimeter=90\div 12=7.5$ feet

So the perimeter is 7 feet and 6 inches, which is between 7 and 8 feet.

Compare your answer with the correct one above

Question

Perimeter of a rectangle is 36 inches. If the width of the rectangle is 3 inches less than its length, give the length and width of the rectangle.

Answer

Let:

$Length=x\Rightarrow Width=x-3$

The perimeter of a rectangle is , where is the length and is the width of the rectangle. The perimeter is known so we can set up an equation in terms of and solve it:

$\Rightarrow2x+2x-6=36$

$\Rightarrow 4x-6=36$

$\Rightarrow 4x=42$

$\Rightarrow x=10.5$

So we can get:

inches

inches

Compare your answer with the correct one above

Question

Which of these polygons has the same perimeter as a rectangle with length 55 inches and width 15 inches?

Answer

The perimeter of a rectangle is twice the sum of its length and its width; a rectangle with dimensions 55 inches and 15 inches has perimeter

inches.

All of the polygons in the choices are regular - that is, all have congruent sides - and all have sidelength two feet, or 24 inches, so we divide 140 by 24 to determine how many sides such a polygon would need to have a perimeter equal to the rectangle. However,

$140 \div 24 = 5 \frac{5}{6}$ ,

so there cannot be a regular polygon with these characteristics. All of the choices fail, so the correct response is that none are correct.

Compare your answer with the correct one above

Question

The length and width of a rectangle are and . Give its perimeter in terms of .

Answer

A rectangle has perimeter , the length and the width. Substitute and in the perimeter formula, and simplify.

$= 2 \left ( x+16\right ) + 2 \left ( 2x-7\right )$

$= 2 \cdot x+2 \cdot 16 +2 \cdot 2x-2 \cdot 7$

Compare your answer with the correct one above

Question

A rectangle has length 30 inches and width 25 inches. Which of the following is true about its perimeter?

Answer

In inches, the perimeter of the rectangle can be calculated by substituting in the following formula:

$P = 2 (30 + 25) = 2\times 55 = 110$

The perimeter is 110 inches.

Now divide by 12 to convert to feet:

$110 \div 12 = 9 \textrm{ R }2$

This makes the perimeter 9 feet 2 inches, which is between 9 feet and 10 feet.

Compare your answer with the correct one above

Question

The length and width of a rectangle are and , respectively. Give its perimeter in terms of .

Answer

The perimeter of a rectangle is , where is the length and is the width of the rectangle. In order to find the perimeter we can substitute the and in the perimeter formula:

Compare your answer with the correct one above

Question

The length of a rectangle is and the width of this rectangle is meters shorter than its length. Give its perimeter in terms of .

Answer

The length of the rectangle is known, so we can find the width in terms of :

The perimeter of a rectangle is , where is the length and is the width of the rectangle.

In order to find the perimeter we can substitute the and in the perimeter formula:

Compare your answer with the correct one above

Question

A rectangle has a length of inches and a width of inches. Which of the following is true about the rectangle perimeter if ?

Answer

Substitute to get and :

$W=5t=5\times 4=20$

The perimeter of a rectangle is , where is the length and is the width of the rectangle. So we have:

$P=2L+2W=2\times 25+2\times20=50+40=90$ inches

Now we should divide the perimeter by 12 in order to convert to feet:

$Perimeter=90\div 12=7.5$ feet

So the perimeter is 7 feet and 6 inches, which is between 7 and 8 feet.

Compare your answer with the correct one above

Question

Perimeter of a rectangle is 36 inches. If the width of the rectangle is 3 inches less than its length, give the length and width of the rectangle.

Answer

Let:

$Length=x\Rightarrow Width=x-3$

The perimeter of a rectangle is , where is the length and is the width of the rectangle. The perimeter is known so we can set up an equation in terms of and solve it:

$\Rightarrow2x+2x-6=36$

$\Rightarrow 4x-6=36$

$\Rightarrow 4x=42$

$\Rightarrow x=10.5$

So we can get:

inches

inches

Compare your answer with the correct one above

Tap the card to reveal the answer