Question

1. the length of a rectangle is 5 centimeters less than twice its width. the perimeter of the rectangle is 80 cm. what are the dimensions of the rectangle?

length = 22 cm, width = 18 cm
length = 24 cm, width = 16 cm
length = 23 cm, width = 14 cm
length = 25 cm, width = 15 cm

Explanation:

Step1: Set up equations

Let the width be \( w \) cm. The length \( l = 2w - 5 \). The perimeter formula for a rectangle is \( P=2(l + w) \). Given \( P = 80 \) cm, so \( 80=2((2w - 5)+w) \).

Step2: Simplify the equation

First, simplify inside the parentheses: \( (2w - 5)+w=3w - 5 \). Then the equation becomes \( 80 = 2(3w - 5) \). Distribute the 2: \( 80=6w - 10 \).

Step3: Solve for \( w \)

Add 10 to both sides: \( 80 + 10=6w-10 + 10 \), so \( 90 = 6w \). Divide both sides by 6: \( w=\frac{90}{6}=15 \) cm.

Step4: Find the length

Substitute \( w = 15 \) into \( l = 2w - 5 \). Then \( l=2\times15 - 5=30 - 5 = 25 \) cm.

Answer:

length = 25 cm, width = 15 cm