length of triangle sides

matteric92

New member
Ok, here's the question:

"The length of the hypotenuse of a right triangle is 4 cm more than the longer leg. The length of the longer leg is 14 cm more than the length of the shorter leg. Find the number of centimeters in the length of each side of the right triangle."

I know the answers are 16, 30, 34, but I have to show my work, and when I use the "a^2 + b^2 = c^2" formula, I always get the answer "sqrt". What am I doing wrong?

This is what I do:

. . .x^2 + (x + 14)^2 = (x + 18)^2
. . .2x^2 + 196 = x^2 + 324
. . .x^2 = 128
. . .x = ????

stapel

Super Moderator
Staff member
Hint: (a + b)<sup>2</sup> = (a + b)(a + b) = a<sup>2</sup> + 2ab + b<sup>2</sup>. It is not equal to a<sup>2</sup> + b<sup>2</sup>.

Eliz.

TchrWill

Full Member
matteric92 said:
"The length of the hypotenuse of a right triangle is 4 cm more than the longer leg. The length of the longer leg is 14 cm more than the length of the shorter leg. Find the number of centimeters in the length of each side of the right triangle."

I know the answers are 16, 30, 34, but I have to show my work, and when I use the "a^2 + b^2 = c^2" formula, I always get the answer "sqrt". What am I doing wrong?

This is what I do:

. . .x^2 + (x + 14)^2 = (x + 18)^2
. . .2x^2 + 196 = x^2 + 324
. . .x^2 = 128
You started out right with x^2 + (x + 14)^2 = (x + 18)^2
Expanding
x^2 + x^2 + 28x += 196 = x^2 + 36x + 324

Collecting terms;
x^2 - 8x - 128 = 0