SOLUTION: The sidewalk on a college campus makes the shape of an L. The sidewalk was constructed such that the length of one side of the L is two times as long as the other side of the L. Th

Question 172215: The sidewalk on a college campus makes the shape of an L. The sidewalk was constructed such that the length of one side of the L is two times as long as the other side of the L. The length of the diagonal sidewalk that connects the ends of the L is 102 feet. Find values for both sides of the L.
A^2 + B^2 = 102^2
A = 2B
(2B)^2 + B^2 = 102^2
4B^2 + B^2 = 102^2
5B^2 = 102^2
5B = Sqrt(102^2)
5B = 102
B = 102/5
B = 20.4
A = 20.4*2
A = 40.8
40.8^2 + 20.4^2 does not equal 102^2 =(

Answer by actuary(112) (Show Source): You can put this solution on YOUR website!
The length of side A (leg of the triangle) is L ft. The length of side B (other leg of the triangle) is 2L ft. The length of the hypotenuse is 102 ft. Using the Pythagorean Theorem, L^2 +(2*L)^2 = 102^2 ft. Therefore, L^2 + 4L^2 = 102^2. So 5*L^2 = 102^2 ft or L = 102/ (Square Root[5]) = 102/2.24= 45.62 ft
Checking the result we have 2*L=2*(45.62 ft) = 91.24 ft.
L^2 = 2081.18
(2L)^2 = 8324.74 L^2 +(2*L)^2 = 2081.18 + 8324.74 = 10405.9
102^2 = 10404 (Difference is due to rounding)
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