Question

A triangle has sides that measure 4 feet, 6 feet, and 9 feet. Find the shortest side of a similar triangle whose longest side measures 16 feet. Round your answer to the nearest tenth.

a) 2.8 feet
b) 4.2 feet
c) 3.5 feet
d) 5.6 feet

Answer 1

To find the shortest side of a similar triangle, divide the length of the longest side of the larger triangle by the corresponding side of the smaller triangle. Then, multiply the shortest side of the original triangle by the scale factor to find the shortest side of the similar triangle. In this case, the shortest side of the similar triangle is 7.1 feet.

Step-by-step explanation:

To find the shortest side of a similar triangle, we need to find the scale factor between the two triangles. The scale factor is found by dividing the length of the longest side of the larger triangle by the corresponding side of the smaller triangle. In this case, the longest side of the larger triangle is 16 feet, and the corresponding side of the smaller triangle is 9 feet. So the scale factor is 16/9.

To find the shortest side of the similar triangle, we multiply the shortest side of the original triangle by the scale factor. The shortest side of the original triangle is 4 feet, so the shortest side of the similar triangle is (4 * 16/9) = 7.1 feet. Rounding to the nearest tenth, the answer is 7.1 feet.