Question

1. the width of a rectangle is 5x - 4. the perimeter of the rectangle is 14x + 4. what is the length of the rectangle?

a. 2x - 6
b. 2x + 6
c. 9x + 8
d. 9x - 8
k. mitchell (mitchell’s math madhouse), 2013

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \), where \( l \) is the length and \( w \) is the width.

Step2: Substitute known values into the formula

We know \( P = 14x + 4 \) and \( w = 5x - 4 \). Substitute these into the formula:
\( 14x + 4 = 2(l + 5x - 4) \)

Step3: Divide both sides by 2

Divide each side of the equation by 2:
\( \frac{14x + 4}{2} = l + 5x - 4 \)
Simplify the left side: \( 7x + 2 = l + 5x - 4 \)

Step4: Solve for \( l \)

Subtract \( 5x \) from both sides and add 4 to both sides:
\( l = 7x + 2 - 5x + 4 \)
Combine like terms: \( l = 2x + 6 \)

Answer:

b. \( 2x + 6 \)