Question

The perimeter of a rectangle is 42 inches. If the length of the rectangle is 14 inches, which equation could be used to find the width, x? A. 2(x + 14) = 42 B. x + 2(14) = 42 C. 14(x + 2) = 42 D. x + 14 = 42

Answer 1

A. 2(x+14) = 42

(2x = 14
x = 7

2(7) + 2(14) = 14 + 28 = 42)

Answer 2

Option A is correct

equation
`2(x+14)=42` could be used.

Explanation:

Given: The length of a rectangle
`(l)` is 14 inches and perimeter of rectangle is 42 inches.

Perimeter(P)of a rectangle in inches is given by:

`P= (2l+w)` ; where
`l` is the length of the rectangle and w is the width of the rectangle.

Substitute the value of P=42 inches , w =x inches and
`l = 14` inches in the above formula we get;

`42 = 2 \cdot (14+x)`

Divide by 2 on both sides we get;

`21 = 14+x`

On simplify, we get;

x = 21-14 = 7 inches

therefore, the width of the rectangle is, x = 7 inches

Check :

Substitute the value of x =7 in option A.

`2(x+14) =42`

`2(7+14)=42`

`2\cdot 21 =42`

42 = 42

Hence, the only equation that could be used to find the width, x is,
`2(x + 14) = 42`