Question

the area of a rectangle is 300 square meters and its length is 3 times its width. how many meters wide is the rectangle?
a) 10
b) 30
c) 50
d) 100
e) 150

Explanation:

Step1: Set up the equation

Let the width of the rectangle be \(w\). Then the length \(l = 3w\). The area formula for a rectangle is \(A=l\times w\). Substituting \(l = 3w\) and \(A = 300\) into the formula, we get \(300=(3w)\times w\).

Step2: Simplify the equation

Simplify \(300=(3w)\times w\) to \(300 = 3w^{2}\).

Step3: Solve for \(w^{2}\)

Divide both sides of \(300 = 3w^{2}\) by 3. We have \(\frac{300}{3}=w^{2}\), so \(w^{2}=100\).

Step4: Solve for \(w\)

Take the square - root of both sides. Since \(w>0\) (width cannot be negative), \(w=\sqrt{100}\).

Answer:

A. 10