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
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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