SOLUTION: Two rectangles are similar. One is 5 cm by 12 cm. The longer side of the second rectangle is 8 cm greater than twice the shorter side. Find its length and width.

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Question 769007: Two rectangles are similar. One is 5 cm by 12 cm. The longer side of the second rectangle is 8 cm greater than twice the shorter side. Find its length and width.
Answer by ramkikk66(644) About Me  (Show Source):
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Two rectangles are similar. One is 5 cm by 12 cm. The longer side of the second rectangle is 8 cm greater than twice the shorter side. Find its length and width.

Ans:

If 2 rectangles are similar, it means that their sides are proportional to each

other. I.e. if the first rectangle has length and width of L1 and W1, and the 

second one has L2 and W2, L1/W1 = L2/W2.



Here, L1 = 5, W1 = 12



In the second rectangle, let the shorter side (width) be x. Then the longer

side (length) is given to be 2*x + 8



Since the sides are proportional, we get the equation



12%2F5+=+%282%2Ax+%2B+8%29%2Fx Cross multiplying

12%2Ax+=+5%2A%282%2Ax+%2B+8%29+=+10%2Ax+%2B+40 Simplifying

2%2Ax+=+40

x+=+20

Shorter side of second rectangle (width) = 20 cm

Longer side = length = 2*20 + 8 = 48 cm



:)