Question

nick built a fence shaped like the triangle below. if it took nick 2.5 minutes per foot, what was the total amount of time it took to build the fence? 15 feet 9 feet

Explanation:

Step1: Find the length of the unknown side

Use the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \). Let the unknown side be \( a \), \( c = 15 \), \( b=9 \). Then \( a=\sqrt{15^{2}-9^{2}}=\sqrt{(15 + 9)(15 - 9)}=\sqrt{24\times6}=\sqrt{144}=12 \) feet.

Step2: Calculate the perimeter of the triangle

The perimeter \( P=a + b + c=12+9 + 15=36 \) feet.

Step3: Calculate the total time

Since it takes \( 2.5 \) minutes per foot, the total time \( T=2.5\times36 = 90 \) minutes.

Answer:

\( 90 \) minutes