The width of a rectangle is 8 inches more than its length. The perimeter of the rectangle is 24 inches. What are the width and length of the rectangle?

Answer 1

Hi,

width is W and length is L

The width of a rectangle is 8 inches more than its length.

this sentence is meaning W = 8 + L 1

on the other hand, perimeter is 24 inches

you know the perimeter = 2 W + 2 L = 24

Now, replace 1 to the perimeter, it means:

2( 8 + L) + 2L = 24

16 + 2L + 2L = 24

4 L = 24 - 16 =8 both side divided by 4

L = 2 then W = 8+ 2 = 10

I hope it was useful, let me know if you have any question.

Minoo

Answer 2

So here we have an algebraic expression needing to be solved, and we need to know a little about rectangles and perimeters to do it:

The perimeter is the sum of all the lengths of the sides of an object, here we will have the sum of the 4 sides of this rectangle be equal to the perimeter. In a 2D rectangle, there are two lengths (L) and two widths (w):

Perimeter = L + L + w + w

But we also know that the width (w) is 8 inches more than the length (L); we can write this relationship as:

w = L + 8

Now that we have an expression for w, lets plug that into the first equation for perimeter:

Perimeter = L + L + (L + 8) + (L + 8)

Now lets simplify:

Perimeter = L + L + L + 8 + L + 8 = 4L + 16

We were also told that the perimeter is equal to 24, so lets make "perimeter" equal 24 in the above equation:

24 = 4L + 16

Now subtract 16 from both sides:

8 = 4L

Now divide both sides by 4

2 = L

Now we know the length is 2, and we know the width (w) is 8 inches more than the length (L), so we know:

w = L + 8

w = 2 + 8

w = 10

Now we know that the width is 10 and the length is 2, and we have solved the problem.

Answer 3

Length is L, width is L+8

2L + 2(L+8) = 24

2L + 2L + 16 = 24

4L + 16 = 24

4L = 8

L=2

length is 2, width is 10, perimeter is 24 and area is 20.