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?

1 Answer
Dec 7, 2017

The width is 99 cm

Explanation:

If the width is ww, then the length is 4w+64w+6 and the perimeter is:

102 = 2w+2(4w+6) = 10w+12102=2w+2(4w+6)=10w+12

Subtracting 1212 from both ends, we find:

10w = 9010w=90

Dividing both sides by 1010, we get:

w = 9w=9

Then the length is 4w+6 = 4(color(blue)(9))+6 = 36+6 = 424w+6=4(9)+6=36+6=42

and the area is w(4w+6) = color(blue)(9) * color(blue)(42) = 378w(4w+6)=942=378 square centimetres - as expected.