Question

set up two equations with two variables. solve using substitution or elimination.

1. the perimeter of a rectangle is 54 cm. the width is 7 less than the length. what is the length and width of the rectangle?

Explanation:

Step1: Define variables

Let \( l \) be the length and \( w \) be the width of the rectangle.

Step2: Set up equations

• From the perimeter formula \( P = 2(l + w) \), with \( P = 54 \), we get \( 2(l + w)=54 \), simplifying to \( l + w = 27 \).
• From "width is 7 less than length", we get \( w = l - 7 \).

Step3: Substitute and solve

Substitute \( w = l - 7 \) into \( l + w = 27 \):
\( l + (l - 7)=27 \)
\( 2l - 7 = 27 \)
\( 2l = 34 \)
\( l = 17 \).

Step4: Find width

Substitute \( l = 17 \) into \( w = l - 7 \):
\( w = 17 - 7 = 10 \).

Answer:

Length is \( 17 \) cm, Width is \( 10 \) cm.