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?
a + b + c = 112 where a,b are the legs and c is the hypotenuse
a + b = 112 - c square both sides
a^2 + 2ab + b^2 = c^2 - 224c + 12544
Note that a^2 + b^2 = c^2 so the above becomes
2ab = 12544 - 224c (1)
The area of the triangle is (1/2) ac
Also the area is (1/2)13.44 * c
(1/2)ab = (1/2) 13.44c
ab = 13.44c
2ab = 26.88c (2)
Sub (2) into (1)
26.88c = 12544 - 224c add 224c to both sides
26.88 c + 224c = 12544
250.88 c = 12544 divide both sides by 250.88
c = 50 = the hypotenuse length