Question

Tyrone is working with two other students to build a border around the school’s triangular garden. Each student brought in one side of the border, but they all used different units to measure the side lengths. The first side is 312 inches long, the second side is 20 feet long, and the third side is 12 yards long. If the measurements need to be in feet, will the three border pieces make a right triangle?

Convert the first side into feet using a proportion.

Answer 1

NO, the these three border pieces will not make a right triangle

Explanation:

Perform the necessary conversions:

1. 312 in converts to

312 in 1 ft

----------- * ------- = 26 ft

12 in 1

2. 20 ft

3. 12 yd converts to

12 yd 3 ft

------------- * --------- = 36 ft

1 yd 1

So the three different side lengths are 26 ft, 20 ft and 36 ft.

For the three pieces to make a right triangle, these measurements must satisfy the Pythagorean Theorem:

26² + 20² = 36², or 1296

676 + 400 = 1076

The Theorem is NOT satisfied, and so NO, the these three border pieces will not make a right triangle.