Answer :
To find the width of the rectangle, we need to use the given information and set up an equation. Let's denote the width of the rectangle as [tex]\( w \)[/tex] inches.
The length of the rectangle is given as 5 inches longer than the width. Therefore, the length can be expressed as [tex]\( w + 5 \)[/tex] inches.
The perimeter [tex]\( P \)[/tex] of a rectangle is calculated using the formula:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]
We are given that the perimeter is 40 inches. Plugging in the values we have:
[tex]\[ 40 = 2 \times (w + (w + 5)) \][/tex]
Simplify the equation inside the parentheses:
[tex]\[ 40 = 2 \times (2w + 5) \][/tex]
Next, distribute the 2:
[tex]\[ 40 = 4w + 10 \][/tex]
To isolate [tex]\( w \)[/tex], subtract 10 from both sides:
[tex]\[ 30 = 4w \][/tex]
Now, divide by 4:
[tex]\[ w = \frac{30}{4} \][/tex]
Simplify the division:
[tex]\[ w = 7.5 \][/tex]
Therefore, the width of the rectangle is [tex]\( 7.5 \)[/tex] inches. The correct answer is:
(A) 7.5
The length of the rectangle is given as 5 inches longer than the width. Therefore, the length can be expressed as [tex]\( w + 5 \)[/tex] inches.
The perimeter [tex]\( P \)[/tex] of a rectangle is calculated using the formula:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]
We are given that the perimeter is 40 inches. Plugging in the values we have:
[tex]\[ 40 = 2 \times (w + (w + 5)) \][/tex]
Simplify the equation inside the parentheses:
[tex]\[ 40 = 2 \times (2w + 5) \][/tex]
Next, distribute the 2:
[tex]\[ 40 = 4w + 10 \][/tex]
To isolate [tex]\( w \)[/tex], subtract 10 from both sides:
[tex]\[ 30 = 4w \][/tex]
Now, divide by 4:
[tex]\[ w = \frac{30}{4} \][/tex]
Simplify the division:
[tex]\[ w = 7.5 \][/tex]
Therefore, the width of the rectangle is [tex]\( 7.5 \)[/tex] inches. The correct answer is:
(A) 7.5
