Asked by Gabby

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?

Answers

Answered by Damon
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
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