Find the lengths of the sides of the triangle.

Question

One leg of a right triangle is 1 millimeter longer than the shorter leg and the hypotenuse is 2 millimeters longer than the longer leg. 

 Find the lengths, The length of the longer leg:  The length of the shorter leg, The length of hypotenuse

 

 

Answer 1

Call the legs a and b.

But b=a+1 and hypotenuse=b+2=a+3, so

(a+3)^2=a^2+(a+1)^2; a^2+6a+9=a^2+a^2+2a+1 (by Pythagoras).

From this we can collect terms together: a^2-4a-8=0.

We can write a^2-4a=8 and add 4 to each side: a^2-4a+4=12:

(a-2)^2=12 and now take square root of each side:

a-2=√12=2√3 (positive square root only because the sides are all positive lengths).

So a=2+2√3, b=3+2√3 and hypotenuse=5+2√3 (all measurements are mm).

Approximately, a=5.464mm, b=6.464mm and hypotenuse=8.464mm.