Question

The length of a rectangle is 9.7 cm more than 4 times the width. if the perimeter of the rectangle is 68.4 cm, what are its dimensions?

Answer 1

P = 2(L + W)
P = 68.4
L = 4W + 9.7

68.4 = 2(4W + 9.7 + W)
68.4 = 2(5W + 9.7)
68.4 = 10W + 19.4
68.4 - 19.4 = 10W
49 = 10W
49/10 = W
4.9 = W <==== the width is 4.9 cm

L = 4W + 9.7
L = 4(4.9) + 9.7
L = 19.6 + 9.7
L = 29.3 <=== the length is 29.3 cm

Answer 2

Let the width of the rectangle = x

4x + 9.7 = length
2(4x + 9.7) + 2x = 68.4
8x + 19.4 + 2x = 68.4
10x = 68.4 - 19.4
x = 49 / 10
x = 4.9 cm

Length
= 4x + 9.7
= 4(4.9) + 9.7
= 29.3 cm

Width = x = 4.9 cm