Find the length and the width...

Question

The perimeter of a certain rectangle is 16 times the width. The length is 12cm more than the width. Find the length and  the widtb of the rectangle.

Answer 1

From the problem we know

P = 16W

L = W + 12

 

We also know

P = 2L + 2W

 

Let's substitute the expressions for P and L in the equation above.

16W = 2(W+12) + 2W

and solve for W

 

 

16W = 2W + 24 + 2W

16W = 4W + 24

12W = 24

W = 2

 

Since L = W + 12

L = 2 + 12

L = 14

 

Now let's check

 

P = 2L + 2W

P = 2(14) + 2(2)

P = 28 + 4 = 32

 

P = 16W

P = 16(2)

P = 32