# 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?

##### 1 Answer
Jun 29, 2016

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:
${h}^{2} = {x}^{2} + {y}^{2}$
${\left(y + 8\right)}^{2} = {y}^{2} + {\left(y - 8\right)}^{2}$
Develop:
${y}^{2} + 16 y + 64 = {y}^{2} + {y}^{2} - 16 y + 64$
${y}^{2} - 32 y = 0$
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.