The longer leg of a right triangle is 8 more than the shorter leg. The hypotenuse is 10 more than the longer leg. Find all three sides.
+128474 shorter side^2 + longer side^2 = hyp ^2
x^2 + (x + 8)^2 = (x + 18)^2
x^2 + x^2 + 16x + 64 = x^2 + 36x + 324 simplify
x^2 - 20x - 260 = 0
Using the Q formula
20 + sqrt [ 20^2 - 4 (1) (-260 ] 20 + sqrt [ 1440]
x = ____________________________ = _______________ =
2 * 1 2
20 + 12 sqrt (10)
______________ = 10 + 6sqrt (10)
2
The sides are
10 + 6sqrt (10)
18 + 6 sqrt (10)
28 + 6sqrt (10)
