Question 1125385: https://vle.mathswatch.co.uk/images/questions/question17405.png please I need help with this homework and I cannot figure this out :) thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe the two rectangles are similar figures, therefore the corresponding sides are proportional.
this means that PQ / AB = QR / BC.
since PQ is 8 and QR is 2, then 8 / AB = 2 / BC.
cross multiply to get 8 * BC = 2 * AB
solve for AB to get AB= 4 * BC.
you are given that the perimeter of ABCD is 60.
this mean that 2 * BC + 2 * AB = 60
since AB = 4 * BC, this becomes 2 * BC + 2 * 4 * BC = 60
combine like terms to get 10 * BC = 60.
solve for BC to get BC = 6.
since AB = 4 * BC, then AB = 24.
the perimeter of ABCD is 60 which means that 2 * AB + 2 * BC = 60 which becomes 2 * 24 + 2 * 6 = 60 which becomes 48 + 12 = 60 which becomes 60 = 60.
this confirms the solution is correct.
in addition, the ratios are good because AB / PQ = 24 / 8 = 3 and BC / QR = 6/3 = 3.
the ratios are the same, confirming that the corresponding sides of the similar figures are proportinal.
your solution is that the length of AB is 24 and the length of BC is 6.
i think it could also be solved as follows:
the perimeter of PQRS is 2 * 8 + 2 * 2 = 16 + 4 = 20
the perimeter of ABCD is 60.
the rectangles are similar so the ratio of corresponding sides has to be the same.
the ratio of the perimeter is 60 / 20 = 3.
the corresponding sides of ABCD have to be 3 times the length of the corresponding sides of PQRS, therefore AB = 3 * 8 = 24 and BC = 3 * 2 = 6.
either way, i'm pretty sure that's the answer you're looking for.
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