Solve for the height of the second rectangle.

Perimeter = 2B + 2H

12 = 2(4) + 2H

12 = 8 + 2H

4 = 2H

H = 2

If they are similar, then the base and height are proportionally equal.

B₁/H₁ = B₂/H₂

4/2 = B₂/H₂

2 = B₂/H₂

B₂ = 2H₂

Use perimeter equation then solve for H:

Perimeter = 2B + 2H

36 = 2 B₂ + 2 H₂

36 = 2 (2H₂) + 2 H₂

36 = 4H₂ + 2 H₂

36 = 6H₂

H₂ = 6

Given that w = 2x and l = 1.5w + 5, a substitution will show that l = 1.5(2x) + 5 = 3x + 5.  

P = 2w + 2l = 2(2x) + 2(3x + 5) = 4x + 6x + 10 = 10x + 10 = 10(x + 1)

The perimeter of a figure is the sum of the lengths of all of its sides. The perimeter of this figure is √27 + 2√3 + √27 + 2√3. But, √27 = √9√3 = 3√3 . Now all of the sides have the same number underneath of the radical symbol (i.e. the same radicand) and so the coefficients of each radical can be added together. The result is that the perimeter is equal to 10√3.

Divide the area of the rectangle by the width in order to find the length of 14 feet. The perimeter is the sum of the side lengths, which in this case is 14 feet + 4 feet +14 feet + 4 feet, or 36 feet.

Area of rectangle:  A = lw

Perimeter of rectangle:  P = 2l + 2w

w = width and l = w + 3

So A = w(w + 3) = 40 therefore w² + 3w – 40 = 0

Factor the quadratic equation and set each factor to 0 and solve.

w² + 3w – 40 = (w – 5)(w + 8) = 0 so w = 5 or w = -8. 

The only answer that makes sense is 5.  You cannot have a negative value for a length.

Therefore, w = 5 and l = 8, so P = 2l + 2w = 2(8) + 2(5) = 26 in.

Perimeter of a quadrilateral is found by adding up the lengths of its sides. The formula for the perimeter of a rectangle is .

Leaving the width to be x, the length is 4x. The total perimeter is 4x + 4x + x + x = 10x.

We divide 25 by 10 to get 2.5, the time required to walk the width.  Therefore the time required to walk the length is (4)(2.5) = 10.

Let l be the length of the garden and w be the width. 

By the specifications of the problem, l = 2w-3.

Plug this in for length in the area formula:

A = l  x w = (2w - 3) x w = 9

Solve for the width:

2w²- 3w - 9 =0 

(2w + 3)(w - 3) = 0

w is either 3 or -3/2, but we can't have a negative width, so w = 3.

If w = 3, then length = 2(3) - 3 = 3.

Now plug the width and length into the formula for perimeter:

P = 2 l + 2w = 2(3) + 2(3) = 12

We define the variables as  and .

We substitute these values into the equation for the area of a rectangle and get . 

 or 

Lengths cannot be negative, so the only correct answer is . If , then . 

Therefore, .

When two polygons are similar, the lengths of their corresponding sides are proportional to each other.  In this diagram, AC and EG are corresponding sides and AB and EF are corresponding sides. 

To solve this question, you can therefore write a proportion:

AC/EG = AB/EF ≥ 3/6 = 5/EF

From this proportion, we know that side EF is equal to 10.