Question

the length of a rectangle is six times its width. if the area of the rectangle is 150 m², find its perimeter.

Explanation:

Step1: Let width be \(w\).

Let the width of the rectangle be \(w\) meters. Then the length \(l = 6w\) meters.

Step2: Use area formula.

The area formula of a rectangle is \(A=l\times w\). Substituting \(l = 6w\) and \(A = 150\) into the formula, we get \(150=6w\times w=6w^{2}\).

Step3: Solve for \(w\).

Divide both sides of the equation \(6w^{2}=150\) by 6: \(w^{2}=\frac{150}{6}=25\). Then take the square - root of both sides. Since \(w>0\) (width cannot be negative), \(w = 5\) meters.

Step4: Find the length.

Since \(l = 6w\), when \(w = 5\), \(l=6\times5 = 30\) meters.

Step5: Calculate the perimeter.

The perimeter formula of a rectangle is \(P = 2(l + w)\). Substitute \(l = 30\) and \(w = 5\) into the formula: \(P=2(30 + 5)=2\times35=70\) meters.

Answer:

70 m