Question

the perimeter of a rectangle is 82 cm. if the length is 14 cm, how wide is the rectangle? a) first write an equation you can use to answer this question. use w as your variable in the equation. the equation is blank b) solve your equation in part a to find the width of the rectangle. answer: the rectangle is blank cm wide.

Explanation:

Part A

Step1: Recall perimeter formula for rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Let length \( l = 14 \) cm, width \( = w \) cm, and \( P = 82 \) cm.

Step2: Substitute values into formula

Substitute \( P = 82 \), \( l = 14 \), and \( w \) into the formula: \( 82 = 2\times(14 + w) \) or \( 2(14 + w)=82 \) (either form is correct).

Step1: Divide both sides by 2

Starting with \( 2(14 + w)=82 \), divide both sides by 2: \( \frac{2(14 + w)}{2}=\frac{82}{2} \), which simplifies to \( 14 + w = 41 \).

Step2: Subtract 14 from both sides

Subtract 14 from both sides: \( 14 + w - 14 = 41 - 14 \), so \( w = 27 \).

Answer:

\( 2(14 + w) = 82 \) (or equivalent like \( 2\times14 + 2w = 82 \))

Part B