A canvas tarp is cut into the shape of a right triangle. The area of the tarp is 60 square… — Armed Services Vocational Aptitude Battery (ASVAB)

A canvas tarp is cut into the shape of a right triangle. The area of the tarp is $60$ square feet, and its shortest leg measures $8$ feet. What is the perimeter of the tarp in feet?

A
$23$
$40$ Answer
C
$46$
D
$60$

Answer

40

To find the perimeter, all three sides of the right triangle are needed. Using the given area (

60

) and shortest leg (

8

), the length of the other leg is found with the area formula

A = \frac{1}{2}bh

, yielding

15

feet. Next, the Pythagorean theorem (

8^2 + 15^2 = c^2

) reveals the hypotenuse is

17

feet. Summing the three sides (

8 + 15 + 17

) gives the correct perimeter of

40

feet.

Step-by-Step Solution

Find the length of the other leg using the area formula for a triangle,

A = \frac{1}{2}bh

60 = \frac{1}{2}(8)b \Rightarrow 60 = 4b \Rightarrow b = 15

feet.

The perimeter requires all three side lengths, so the missing leg must be calculated first.

Use the Pythagorean theorem (

a^2 + b^2 = c^2

) to find the hypotenuse.

8^2 + 15^2 = c^2 \Rightarrow 64 + 225 = c^2 \Rightarrow 289 = c^2 \Rightarrow c = 17

feet.

The hypotenuse is the third side needed to find the complete outer boundary of the right triangle.

Calculate the perimeter by summing the three side lengths.

P = 8 + 15 + 17 = 40

feet.

The perimeter of any polygon is the total length of its outer boundary.

Key Concept

Calculating missing dimensions of a right triangle using area and the Pythagorean theorem to find the perimeter.

Estimated Time:1m 0s

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