Question

1. the length of a rectangle is 5 less than twice its width. the perimeter is 26 meters. find the length of the rectangle?

objective 3: given a formula, students will be able to solve for a given variable
★ given a mathematical formula you can solve for the identified variable

Explanation:

Step1: Define variables

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

Step2: Use the perimeter formula

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

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Step3: Solve for \(w\)

Add \(10\) to both sides: \(26 + 10=6w-10 + 10\), so \(36 = 6w\). Then divide both sides by \(6\): \(w=\frac{36}{6}=6\).

Step4: Find the length

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

Answer:

The length of the rectangle is \(7\) meters.