A rectangle has a length that is 7cm more than twice the width. The area of the rectangle is 60cm squared. Find the dimensions of the rectangle.


From Stephanie
Grade 10

Hi Stephanie,

Rather than do your homework problem for you I am going to solve a similar problem.

A rectangle has a length that is 5 cm less than three times the width. The area of the rectangle is 250 cm squared. Find the dimensions of the rectangle.

I am going to use L for the length of the rectangle and W for the width. I know that L is 5 cm less than three times W so

L is 5 cm less than 3W, that is
L = 3W - 5

I also know that the area is 250 cm squared and the area of a rectangle is the length times the width. Thus

L W = 250, that is
(3W - 5) W = 250

Expanding this I get

3W² - 5W = 250, or
3W² - 5W - 250 = 0

Factoring I get

(3W + 25)(W - 10) = 0

Thus W = ^-25/₃ or W = 10

Since W is the width of a rectangle it can't be negative and hence W = 10 cm.

Since L = 3W - 5, L = 30 - 5 = 25 cm.

Now check:

Is the length that is 5 cm less than three times the width? Yes, 25 cm is 5 cm less that 3 times 10 cm.
Is the area of the rectangle is 250 cm squared? Yes, L W = 10 25 = 250 cm squared.

Now try your problem and make sure you check your answer.

Penny