A right triangle has a hypotenuse that is 6 m longer than 2 times the shortest side and the third side is 2 m shorter than the hypotenuse. Find the area of the triangle.
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A right triangle has a hypotenuse that is 6 m longer than 2 times the shortest side and the third side is 2 m shorter than the hypotenuse. Find the area of the triangle.
c2 = a2 + b2
c = hypotenuse = (2a + 6)
a = short side
b = (hyp – 2) = (2a + 6) – 2
(2a + 6)2 = a2 + ((2a + 6) – 2)2
(2a + 6)2 = a2 + (2a + 4)2
4a2 + 24a + 36 = a2 + 4a2 + 16x + 16
–a2 + 8x + 20 = 0
a2 – 8x – 20 = 0
(a + 2)(a – 10) = 0
a = – 2 , , , discard
a = 10
b = (2a + 4) = (20 + 4)
b = 24
c = (2a + 6) = (20 + 6)
c = 26
check if these are plausible numbers: 262 =? 102 + 242
676 =? 100 + 576 Looks good, so continue.
A = (1/2)(base)(height)
A = (1/2)(10)(24)
A = 120
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