Question

the length of a rectangle is 5 centimeters less than twice the width. the perimeter of the rectangle is 26 cm. what are the dimensions of the rectangle? can you use an equation to determine the dimensions of th rectangle?

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) cm. Then the length \( l=(2w - 5) \) cm.

Step2: Use the perimeter formula

The perimeter formula of a rectangle is \( P = 2(l + w) \). Given \( P = 26 \) cm. Substitute \( l=(2w - 5) \) into the formula:

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Step3: Solve for \( w \)

Add 10 to both sides of the equation \( 26 = 6w-10 \):

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Divide both sides by 6: \( w=\frac{36}{6}=6 \)

Step4: Solve for \( l \)

Substitute \( w = 6 \) into \( l=(2w - 5) \): \( l=2\times6-5=12 - 5=7 \)

Answer:

The width of the rectangle is \( 6 \) cm and the length is \( 7 \) cm.