# 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

Algebra ->  Algebra  -> Pythagorean-theorem -> 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      Log On

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 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)