The hypotenuse of a right triangle is 5 ft. long. What are the lengths of the two legs if their sum is 6 ft. long?

Answer 1

hypotenuse = 5

h^2 = x^2 + y^2 where x and y are the two other sides of the right triangle

x+y = 6

y=6-x

5^2 = x^2 + (6-x)^2

25 = x^2 +x^2 -12x + 36

2x^2 -12x = -11

x^2 -6x = -11/2

x^2 -6x + 9 = -11/2 + 9

(x-3)^2 = -11/2 +9 = 7/2

x-3 = + or - sqr(7/2)

x = 3 + or - sqr(7/2

= about 3 + or - 1.87

= about 4.87 or 1.13

y=6-4.87= 1.13 or 6-1.13=4.87

the other two sides are about 4.87 feet and 1.13 feet

check the answer:

4.87^2 + 1.13^2 = 23.72 + 1.28 = 25 = 5^2 = hypotenuse squared.