The hypotenuse of a right triangle is 26yards long.one leg is 14 yards longer than the other.find the length?

Question

Find the length of the legs.

Round irrational solutions to the nearest hundredth.

Answer 1

The hypotenuse of a right triangle lenght  is 26yards and one leg lenght  is 14 yards

Apply pythagorean formula c^2 = a^2+b^2

Where c = 26 , a = x  and b = x+14

x^2 + (x + 14)^2 = 26^2

x^2 + x^2 + 28x + 196 = 676

2x^2 + 28x - 480 = 0

x^2 + 14x - 240 = 0

x^2+ 24x-10x - 240 = 0

x(x+24) - 10 (x+24) = 0

(x + 24)(x - 10) = 0

x + 24 = 0 or x - 10 = 0

x = -24 or x = 10

But a negative length makes no sense, so we can discard the negative solution.

x = 10, so the shorter leg is 10 yards long.

x + 14 = 24, so the longer leg is 24 yards long.