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Intermediate Geometry : How to find the perimeter of an acute / obtuse triangle

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

For the triangle below, the perimeter is . Find the value of .

Possible Answers:

Correct answer:

Explanation:

The dashes on the two sides of the triangle indicate that those two sides are congruent. Thus, the length of the missing side is 2x-5 also.

Now, use the information given about the perimeter to set up an equation to solve for . The sum of all the sides will give the perimeter.

2x-5+2x-5+x=40

5x-10=40

5x=50

x=10

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Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Find the value of if the perimeter is .

Possible Answers:

Correct answer:

Explanation:

The dashes on the two sides of the triangle indicate that those two sides are congruent. Thus, the length of the missing side is x+3 also.

Now, use the information given about the perimeter to set up an equation to solve for . The sum of all the sides will give the perimeter.

x+3+x+3+x=24

3x+6=24

3x=18

x=6

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Example Question #2 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Find the value of if the perimeter is .

Possible Answers:

Correct answer:

Explanation:

The dashes on the two sides of the triangle indicate that those two sides are congruent. Thus, the length of the missing side is 2x-2 also.

Now, use the information given about the perimeter to set up an equation to solve for . The sum of all the sides will give the perimeter.

2x-2+2x-2+3x-6=39

7x-10=39

7x=49

x=7

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Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

An acute isosceles triangle has an area of square units and a base with length . Find the perimeter of this triangle.

Possible Answers:

$\sqrt{73}+8$

$2\sqrt{73} +6$

$\sqrt{73}+6$

$2\sqrt{73}+8$

Correct answer:

$2\sqrt{73} +6$

Explanation:

To solve this problem, first work backwards using the formula:

$Area=\frac{b\cdot h}{2}$

Plugging in the given information and solving for height.

$24=\frac{6h}{2}$

$24\times2=6h$

48=6h

$h=\frac{48}{6}=8$

Now that you've found the height of the triangle, use the Pythagorean Theorem to find the length of one of the equivalent sides of the triangle.

(Note, when applying the formula divide the measurement of the base in half--so the triangle will have sides of 3, 8 and c^2 .

Thus, the solution is:
3^2+8^2=c^2
9+64=c^2
73=c^2

$c=\sqrt{73}$

In this problem, the isosceles triangle will have two sides with the length of $\sqrt{73}$ and one side length of . Therefore, the perimeter is: $2\sqrt{73}+6$

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Example Question #3 : How To Find The Perimeter Of An Acute / Obtuse Triangle

A scalene triangle has sides with lengths of $\frac{3}{4}$ foot, $\frac{1}{4}$ foot, and $\frac{2}{6}$ foot. Find the perimeter of the the triangle (in inches).

Possible Answers:

18in

16in

12in

24in

Correct answer:

16in

Explanation:

To solve this problem, first convert each of the fractions from feet to inches.

$\frac{3}{4}=\frac{9}{12}=9$ inches

$\frac{1}{4}=\frac{3}{12}=3$ inches

$\frac{2}{6}=\frac{4}{12}=4$ inches

The perimeter of the triangle must equal 9+3+4=16

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Example Question #3 : How To Find The Perimeter Of An Acute / Obtuse Triangle

An acute triangle has side lengths of and . The hypotenuse of the triangle is not . Find the perimeter of this triangle.

Possible Answers:

$3\sqrt{41}$

$\sqrt{41}+27$

$3\sqrt{41}+27$

Correct answer:

$3\sqrt{41}+27$

Explanation:

Since the two side lengths provided in the question are not the hypotenuse, first use the Pythagorean Theorem to find the length of the third side.

a^2+b^2=c^2

12^2+15^2=c^2

144+225=c^2

c^2=369

$c=\sqrt{369}=\sqrt{9}\sqrt{41}=3\sqrt{41}$

The perimeter is equal to a+b+c .

$12+15+3\sqrt{41}$

$3\sqrt{41}+27$

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Example Question #4 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Inter_geo_tri_series_

Find the perimeter of the triangle shown above.

Possible Answers:

$4.5+\sqrt{26.5}in$

$\sqrt{26.5}in$

$\sqrt{26.5+7}in$

$7+\sqrt{26.5}in$

Correct answer:

$7+\sqrt{26.5}in$

Explanation:

Since the two side lengths provided in the question are not the hypotenuse, first use the Pythagorean Theorem to find the length of the third side.

a^2+b^2=c^2

2.5^2+4.5^2=c^2

6.25+20.25=c^2

c^2=26.5

$c=\sqrt{26.5}$

Perimeter is equal to a+b+c .

$2.5+4.5+\sqrt{26.5}=7+ \sqrt{26.5}$

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Example Question #5 : How To Find The Perimeter Of An Acute / Obtuse Triangle

An obtuse Isosceles triangle has an area of square units and a base with length . Find the perimeter of this triangle.

Possible Answers:

$4+\sqrt{5}$

$8+8\sqrt{5}$

$8+2\sqrt{5}$

$4\sqrt{5}$

Correct answer:

$8+8\sqrt{5}$

Explanation:

To solve this solution, first work backwards using the formula: $Area=\frac{b\cdot h}{2}$

$32=\frac{8h}{2}$

8h=64

h=8

Now that you've found the height of the triangle, use the Pythagorean Theorem to find the length of one of the equivalent sides of the triangle.

(Note, when applying the formula divide the measurement of the base in half--so the triangle will have sides of 4,8 and c^2 .

Thus, the solution is:
4^2+8^2=c^2

16+64=c^2

c^2=80

$c=\sqrt{80}=4\sqrt{5}$

In this problem, the isosceles triangle will have two sides with the length of $4\sqrt{5}$ and one side length of . Therefore, the perimeter is: $8+8\sqrt{5}$ .

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Example Question #6 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Inter_geo_tri_series_

Find the perimeter of the acute isosceles triangle shown above. Note, the triangle has a base of and height of .

Possible Answers:

$14\sqrt{449}$

$14+2\sqrt{449}$

$14+\sqrt{449}$

$\sqrt{449}$

Correct answer:

$14+2\sqrt{449}$

Explanation:

Use the Pythagorean Theorem to find the length of one of the equivalent sides of the triangle.

(Note, when applying the formula divide the measurement of the base in half--so the triangle will have sides of 7,20 and c^2 .

Thus, the solution is:
7^2+20^2=c^2

49+400=c^2

c^2=449

$c=\sqrt{449}$

In this problem, the isosceles triangle will have two sides with the length of $\sqrt{449}$ and one side length of . Therefore, the perimeter is: $14+2\sqrt{449}$ .

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Example Question #2 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Find the perimeter of the triangle below. Round to the nearest tenths place.

Possible Answers:

22.4

24.5

30.7

25.3

Correct answer:

22.4

Explanation:

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a 30-60-90 triangle, where the long leg is the length of the short leg times $\sqrt3$ and the hypotenuse is two times the length of the short side. We can find out that the height of the triangle is since it is the short leg and the hypotenuse is .

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $6, 6, \text{ and }6\sqrt3$ .

Now, add up these side lengths to find the perimeter.

$\text{Perimeter}=6+6+6\sqrt3=22.4$

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Intermediate Geometry : How to find the perimeter of an acute / obtuse triangle

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #2 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #3 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #3 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #4 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #5 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #6 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #2 : How To Find The Perimeter Of An Acute / Obtuse Triangle

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