One leg of a right triangle is 7 feet longer than the shortest leg. The hypotenuse is 9 feet longer than the shortest leg. Find the lengths of the two legs and the hypotenuse of the triangle.

Question

One leg of a right triangle is 7 feet longer than the shortest leg. The hypotenuse is 9 feet longer than the shortest leg. Find the lengths of the two legs and the hypotenuse of the triangle.

Answer 1

h = 9 +x

x = 7+y

h^2 = x^2 + y^2

(9+x-7)^2 = x^2 + (x-7)^2

4x + 4= x^2 -14x + 49

x^2 -18x +45 = 0

factor

(x-15)(x-3) = 0

x = 15 feet

or

x = 9 +/- .5sqr(18^2 -4(45))=15 feet = longer leg

y = x-7 = 8 feet = shorter leg

h = x+2 = 17 feet= hypotenuse

check

8^2 +15^2 = 64+225 = 289 = 17^2