Question

A lot of people asked this question.. But it is really confusing. Can someone PLEASE give a good explanation?? The length of a rectangle is twice its width. Find its area, if its perimeter is 7 1 3 cm.

Answer 1

Hello from MrBillDoesMath!

Answer:

Area = 28,243 approximately  (assuming that 7 1 3 cm meant 713 cm)

Discussion:

See attachment.  The length of the rectangle (shown as "L") is twice the width (shown as "w"). This means

L = 2w        (A)

We are also told the perimeter (the sum of the side lengths of the rectangle) is 713 cm or

L + w + L + w = 713     => add common terms

2L + 2w = 713.

Substituting (A), above, into this equation gives:

2L       + 2w = 713

2 (2w) + 2w = 713   =>

4w       + 2w = 713   => combine common terms

6w = 713                  => divide both sides by 6

w = 713/6

The original question was to find the area of the rectangle.

A = L w                    => using (A) above                  

A = (2w) w               =>  combine common terms

A = 2w^2                 => as w = 713/6

A = 2 (713/6)^2        => calculator time

A=  2 (14121.4)     approximately

A = 28,243 approximately

Hope this didn't confuse you but the problem has several elements that one needs to deal with.

Thank you,

MrB