Quadrilaterals ABCD and EFGH are similar. The perimeter of ABCD is 40 inches and the perimeter of
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Quadrilaterals ABCD and EFGH are similar. The perimeter of ABCD is 40 inches and the perimeter of EFGH is 16 inches.
Find the ratio of the corresponding side lengths of ABCD to EFGH.
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If two quadrilaterals are similar it means their corresponding angles are equal and the ratio of their corresponding side lengths is constant Lets denote this ratio as r Given that the perimeter of ABCD is 40 inches and the perimeter of EFGH is 16 inches we can express the perimeters in terms of the side lengths Perimeter of ABCD AB BC CD DA 40 inches Perimeter of EFGH EF FG GH HE 16 inches Now lets express the corresponding side lengths of ABCD to EFGH using the ratio r AB r EF BC r FG CD r GH DA r HE We know that the perimeter of ABCD is 40 inches so 40 AB BC CD DA 40 r EF r FG r GH r HE And the perimeter of EFGH is 16 inches so 16 EF FG GH HE Now we have two equations 40 r EF r FG r GH r HE 16 EF FG GH HE To find the ratio r of the corresponding side lengths we can divide the equation 1 by equation 2 4016 r EF r FG r GH r HE EF FG GH HE Simplifying 25 r EF FG GH HE EF FG GH HE Now notice that the terms EF FG GH HE appear on both sides of the equation so they cancel out 25 r Therefore the ratio of the ...View the full answer
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Related Book For
Holt McDougal Larson Geometry
ISBN: 9780547315171
1st Edition
Authors: Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
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