A right angle triangle
The perimeter of a right angle triangle is 112 mm.
The length of the altitude that is perpendicular to the hypotenuse is 13.44 mm.
What is the length, in mm, of the hypotenuse?
Give your answer to 3 decimal places.
The answer is 50.
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1 solution
Let legs = a and b. Let hypotenuse = c.
Then a + b + c = 112, and a^2 + b^2 = c^2.
Area of triangle = .5 * a * b = .5 * 13.44 * c therefore a b = 13.44 c.
a + b = 112 - c
a^2 + 2 a b + b^2 =12544 -224*c +c^2
a^2 + b^2 + 2 a b = 12544 -224*c + c^2
Substituting:
c^2 + 2 * 13.44 *c = 12544 -224 * c + c^2
250.88 *c = 12544
c = 50