Help me solve this question please

Question

The perimeter of a rectangle is 24 inches. Find the dimensions if it’s length is 3 inches greater than it’s width.

a:5.5 and 6.5

b:4.5 and 7.5

c:3.5 and 8.5

d:4 and 7

Answer 1

On an item like this, especially if on a SAT, you would be able to guess and check.

First, reason about the answer options. Which pair of dimensions differ by 3?

Answer: b and d

Second, which pair of dimensions will result in a perimeter of 24?

Answer:

Trying 4.5 and 7.5: 2(4.5) + 2(7.5) = 9 + 15 = 24 <-- CORRECT!

Trying 4 and 7: 2(4) + 2(7) = 8 + 15 = 23 XXX

OR carry out the algebraic analysis:

width = x

length = x+ 3

Perimeter = 24

Perimeter = 2(x) + 2(x + 3) = 2x + 2x + 6 = 4x + 6

4x + 6 = 24

4x = 18

x = 18/4

x = 4.5 <-- width

x + 3 = 7.5 <-- length

Check: 2(4.5) + 2(7.5) = 9 + 15 = 24