Question

A sail on a sailboat is in the shape of two adjacent right triangles. The hypotenuse of the lower triangle is 10 ft, and one leg is 2 ft shorter than the other leg. Find the lengths of the legs of the lower triangle.

Answer 1

Explanation:

The diagram of the sail of the sailboat is shown in attached photo. Let x represent the length of the longer length. If one leg is 2 ft shorter than the other leg, it means that the length if the shorter length is x - 2. We would apply Pythagoras theorem to find the length of the legs of the lower triangle.

Hypotenuse^2 = opposite side^2 + adjacent side^2

10^2 = x^2 + (x + 2)^2

100 = x^2 + x^2 + 2x + 2x + 4

100 = 2x^2 + 4x + 4

2x^2 + 4x + 4 - 100 = 0

2x^2 + 4x - 96 = 0

x^2 + 2x - 48 = 0

x^2 + 8x - 6x - 48 = 0

x(x + 8) - 6(x + 8) = 0

x - 6 = 0 or x + 8 = 0

x = 6 or x= - 8

Since the length cannot be negative, the lengths of the lower triangle are

6 feet and 6-2 = 4 feet