Inspired by Brian Charlesworth
Geometry
Level
pending
A right triangle with perimeter 120 units has sum of the two shorter sides as 70 units . What is the length of the altitude to the longest side of the triangle?
The answer is 24.
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1 solution
Let the length of the two shorter sides be 'a' and 'b' ; and the length of the hypotenuse be 'c' units ; 'x' be the length of the altitude to the hypotenuse(longest side)
It is given that a+b = 70 .....(1)
Using Pythagoras Theorem , c^2=a^2+b^2 .....(2)
Area of the right triangle = (1/2)(ab) = (1/2)(cx) . Or , ab = cx .....(3)
Perimeter = a+b+c = 120 . Or c = 120 - 70 = 50 from eqn(1)
(a+b)^2 = a^2 + b^2 + 2ab
Or , 70^2 = c^2 + 2cx from eqn (1),(2),(3)
Or, 4900 = 2500 + 100x
Or, x =49-25
Or, x=24 which is the length of the altitude to the longest side (hypotenuse).