(2) The hypotenuse of a right triangle has length 20 units. The sum of the lengths of the other 2 sides is 28 units. Find the lengths of the other 2 sides of the triangle.
SOLUTION:
Let the two sides be X and Y
X + Y = 28 ==> X = 28 - Y
202 = X2 + Y2
400 = (28 - Y)2 + y2
400 = 784 - 56Y + 2Y2
2Y2 - 56Y + 384 = 0
Y2 - 28Y + 192 = 0
(Y - 16)(Y - 12) = 0
Y = 16 ==> X = 12
Y = 12 ==> x = 16
The two sides of the triangle have a measure of 16 and 12.