Question

What is the length and the width of the rectangle?

A rectangle has a perimeter of 102 cm and the given area (378 cm). Its length is 6 more than four times its width. What is the length and what is the width of the rectangle?

Answer 1

The width is `9` cm

Explanation:

If the width is `w`, then the length is `4w+6` and the perimeter is:

`102 = 2w+2(4w+6) = 10w+12`

Subtracting `12` from both ends, we find:

`10w = 90`

Dividing both sides by `10`, we get:

`w = 9`

Then the length is `4w+6 = 4(color(blue)(9))+6 = 36+6 = 42`

and the area is `w(4w+6) = color(blue)(9) * color(blue)(42) = 378` square centimetres - as expected.