Question

Can anybody help please?

Answer 1

AB = 24 cm.

BC = 6 cm.

Explanation:

The outer rectangle is a dilation of the inner rectangle centered at the origin. Therefore:

The inner and outer rectangles are similar so the ratio of length to width of the outer rectangle is the same as the ratio of length to width of the inner one.

so AB / BC = 8/2 = 4

AB = 4BC -------------(1)

Also as the perimeter = 60

2AB + 2BC = 60.............(2)

Substituting AB = 4BC in equation (2):

2(4BC) + 2BC = 60

10BC = 60

BC = 6 cm.

and AB = 4*6 = 24 cm.

Answer 2

AB = 24 cm, BC = 6 cm

Explanation:

The perimeter of PQRS = 2(8) + 2(2) = 16 + 4 = 20 cm

Given the perimeter of ABCD is 60 cm, then

scale factor =
`(60)/(20)` = 3

That is the dimensions of ABCD are 3 times those of PQRS, so

AB = 3 × 8 cm = 24 cm

BC = 3 × 2 cm = 6 cm