Question

Rectangle A'B'C'D' is a dilation of rectangle ABCD, and the scale factor is 2. The perimeter of ABCD is 18 mm. The area of ABCD is 20 mm². a. Write an equation for, and calculate, the perimeter of ABCD​

Answer 1

Equation for perimeter of a rectangle = 2(L + W)
where L = length and W = width of the rectangle

Perimeter of A'B'C'D' = 36

Area of A'B'C'D' = 80

Explanation:

Original Rectangle ABCD has perimeter of 18 and area of 20

Perimeter is given by the equation, P = 2(L + W)

So we have, given the data,
P = 2(L+W) = 18

L + W = 9 (1)

Area A = LW = 20 (2)

What combinations of L and W produce L+W = 9 and LW = 20?

Factors of 20 and their sum
1 x 20 Sum = 21
2 x 10 Sum = 12
4 x 5 Sum = 9

So we can say L = 5 and W = 4 (L is usually larger than W)

and the equation becomes

When dilated by a factor of 2 to get rectangle A'B'C'D'

L' = 2L = 2 x 5 = 10
W' = 2W = 2 x4 =8

So

Perimeter of A'B'C'D' = 2(10 + 18) = 36 m
Area of A'B'C'D' = 10 x 8 = 80 mm²