Question

Two rectangles or similar one is 5 cm x 12 cm the long side of the second rectangle is 8 cm greater than twice is short side find its length and width

Answer 1

The length is 48

The width is 20

Explanation:

When 2 rectangles (figures) are similar, the ratio of corresponding sides are equal.

This rectangle is 5 by 12, so the shorter side (corresponding to 5) to the longer side (corresponding to 12) would be the same ratio, 5:12.

Let shorter side be s, and

longer side be l

It says, long side is 8 greater than twice short, we can write this as:

`l=2s+8`

In similar rectangles, we have said the corresponding sides' ratio are equal, so we could write:

`(s)/(l)=(5)/(12)`

Now, we replace the new found expression for "l" onto this and cross multiply and solve for s first:

`(s)/(l)=(5)/(12)\\(s)/(2s+8)=(5)/(12)\\5(2s+8)=12*s\\10s+40=12s\\2s=40\\s=(40)/(2)\\s=20`

So the shorter side is 20. and hence the longer side would be:

l = 2s + 8

l = 2(20) + 8

l = 40 + 8

l = 48

The longer side is 48.

The length is 48

The width is 20