Problema Solution
the hypotenuse of a right triangle is 13 ft long. one leg is 7 ft more than the other leg. Find the length of each leg.
Answer provided by our tutors
let
c = 13 ft the hypotenuse
a and b are the legs, a >0 , b>0
one leg is 7 ft more than the other leg
a = b + 7
using the Pythagorean Theorem we can write
a^2 + b^2 = c^2
substitute a = b + 7 in the above equation
(b + 7)^2 + b^2 = 13^2
by solving the quadratic equation we find and consider the positive root
b = 5 ft
a = 5 + 7 = 12 ft
click here to see step by step solution of the quadratic equation
the legs of the right triangle are 5 ft and 12 ft.