Find the length and width

Question

The length of a rectangle is 8 inches more than the width. The perimeter is 40inches. Find the length and the width of the rectangle

Answer 1

Hi Cate.

 

What we need here is a variable for the width.  Lets say w= width.

 

Now when they tell us that the length "is 8 inches more than the width", we can write length = w+8.

 

The perimeter is the distance around the rectangle, so the perimeter is 2 lengths and 2 widths, so

in "math speak" this would be

 

Perimeter = 2*length + 2 * width.

 

But the length=w+9, and the perimeter is 40",

so we can substitute those into the perimeter equation.

 

40 = 2*(w+8) + 2*w

 

Now distribute the 2 into the (w+8)

 

40 = 2w + 16 + 2w

 

Now combine like terms.

 

40 = 4w + 16

 

Now put all the constants on the left by subtracting 16 from both sides.

 

24 = 4w

 

Now divide both sides by 4 and find that the WIDTH = 6 inches.

Since the length is 8 inches more than the width, then the length is 6 + 8 = 14 inches.

 

Check to see that it works:  Add 2 widths (12 inches) to 2 lengths (28 inches) together.  Do they equal the perimeter of 40"

 

YES!   So we got the problem right!

 

Width = 6 inches.   Length = 14 inches.