Question

A rectangle has a perimeter of 24 inches. The length is 4 inches longer than the width. Find the dimensions of the rectangle.

A. 5 inches by 11 inches
B. 2 inches by 6 inches
C. 5 inches by 9 inches
D. 4 inches by 8 inches

Answer 1

Let l=w+4

24 = (w+4) + (w+4) + w + w

24 = 4w+8

Now just solve for w by first subtracting 8 on each side.
16=4w

Next divide by four on each side
w=4

So the width is 4
Length= width+4

Length is 4+4=8

Answer is D: 4in by 8in

Answer 2

For this case we have that by definition, the perimeter of a rectangle is given by:

`P = 2a + 2b`

Where:

a and b are the sides of the rectangle.

a: It's the long

b: It is the width

As data we have to:

`P = 24\\b = x\\a = 4 + x`

So:

`2 (4 + x) + 2x = 24\\8 + 2x + 2x = 24\\8 + 4x = 24\\4x = 24-8\\4x = 16\\x = \frac {16} {4}\\x = 4`

Thus, the width is 4 and the length is 8.

Answer:

Option D