The longer leg of a right triangle is 8 more than the shorter leg. The hypotenuse is 8 more than the longer leg. Find all three sides.

Guest Oct 15, 2020

edited by
Guest
Oct 15, 2020

#1**+1 **

Let the shorter leg = S

The longer leg = S + 8

The Hypotenuse = S + 16

Pythagoras’s Theorem:

[S + 16]^2 = [S + 8]^2 + S^2

Solve for S:

(S + 16)^2 = S^2 + (S + 8)^2

Expand out terms of the right hand side:

(S + 16)^2 = 2 S^2 + 16 S + 64

Subtract 2 S^2 + 16 S + 64 from both sides:

-64 - 16 S - 2 S^2 + (S + 16)^2 = 0

Expand out terms of the left hand side:

-S^2 + 16 S + 192 = 0

The left hand side factors into a product with three terms:

-(S - 24) (S + 8) = 0

Multiply both sides by -1:

(S - 24) (S + 8) = 0

Split into two equations:

S - 24 = 0 or S + 8 = 0

Add 24 to both sides:

S = 24 or S + 8 = 0

Subtract 8 from both sides:

S = 24 - The short side; 24+8=32 - The longer side;

32 + 8 =40 - The Hypotenuse

Check: 40^2 = 32^2 + 24^2

1600 = 1600

Guest Oct 15, 2020