The length of a hypotenuse of a right triangle is 29 feet. The Altitude drawn perpendicular to the hypotenuse is 10 feet. What are the lengths of the two legs?

Answer 1

by similar triangles
divide hypotenuse into x and 29-x

x/10 = 10/(29-x)

100 = 29 x - x^2
x^2 -29 x + 100 = 0
(x-25)(x-4) = 0

so the little triangle has short arm 4 and the big one has long arm 25

sqrt (100 + 16) = sqrt(116) = 2 sqrt(29)
sqrt (100+625) = sqrt(725) = 5 sqrt(29)

check
4(29) + 25(29) = 29^2 yes