Question

One leg of a right triangle is 8 millimeters shorter than the longer leg and the hypotenuse is 8 millimeters longer than the longer leg. How do you find the lengths of the triangle?

Answer 1

24 mm, 32 mm, and 40 mm

Explanation:

Call x the short leg
Call y the long leg
Call h the hypotenuse
We get these equations
x = y - 8
h = y + 8.
Apply the Pythagor theorem:
`h^2 = x^2 + y^2`
`(y + 8)^2 = y^2 + (y - 8)^2`
Develop:
`y^2 + 16y + 64 = y^2 + y^2 - 16y + 64`
`y^2 - 32y = 0`
y(y - 32) = 0 -->
y = 32 mm
x = 32 - 8 = 24 mm
h = 32 + 8 = 40 mm
Check: (40)^2 = (24)^2 + (32)^2. OK.