The hypotenuse of a right triangle is 17 units long. Find the other two sides if the perimeter of the triangle is 40 units. Separate the numbers by a comma.

Answer 1

Let x and y be the two legs of the right triangle.

By Pythagorean Theorem:

x^2 + y^2 = 289

Also since perimeter = 40:

x + y + 17 = 40

Determine x from 2nd equation:

x = 23 - y

substitute value for x into 1st equation:

(23-y)^2 + y^2 = 289

529 - 46y + y^2 + y^2 = 289

2y^2 - 46y + 240 = 0

y^2 - 23 + 120 = 0

Factor:

(y-15)(y-8) =

If y = 15, then x = 23 - 15 = 8

If y = 8, then x = 23 - 8 = 15

Thus the other two sides must be 15 and 8.

Verify: perimeter is 15 + 8 + 17 = 40 --- check

(15)*2 + (8)^2 = 289 ---- check

y cannot be 40 because the perimeter is 40, so y must be equal to 6.

and x must be equal to 23 - 6 =