Question

the area of a rectangle is 25½ square meters. the length of the rectangle is 8½ meters. what is the width in centimeters?

Explanation:

Step1: Convert mixed numbers to improper fractions

The area formula for a rectangle is \(A = l\times w\). Given \(A = 25\frac{1}{2}=\frac{25\times2 + 1}{2}=\frac{51}{2}\) square - meters and \(l=8\frac{1}{2}=\frac{8\times2+1}{2}=\frac{17}{2}\) meters.

Step2: Solve for the width using the area formula

From \(A = l\times w\), we can solve for \(w\) as \(w=\frac{A}{l}\). Substitute \(A=\frac{51}{2}\) and \(l = \frac{17}{2}\), then \(w=\frac{\frac{51}{2}}{\frac{17}{2}}\).
Using the rule \(\frac{a/b}{c/d}=\frac{a\times d}{b\times c}\), we have \(w=\frac{51\times2}{2\times17}\).
Cancel out the common factor of 2 in the numerator and denominator: \(w=\frac{51}{17}\).
Since \(51\div17 = 3\) meters.

Step3: Convert meters to centimeters

Since \(1\) meter \(= 100\) centimeters, then \(w=3\times100=300\) centimeters.

Answer:

300 centimeters