Question

a rectangles length and width are in a ratio of 7:2. the area is 350 square meters. what are the length and width? length = meters width = meters

Explanation:

Step1: Set up variables

Let the length be \(7x\) meters and the width be \(2x\) meters. The area formula for a rectangle is \(A = length\times width\).

Step2: Substitute into the area formula

We know \(A = 350\), so \(350=(7x)\times(2x)\). Simplify the right - hand side: \((7x)\times(2x)=14x^{2}\). Then the equation becomes \(14x^{2}=350\).

Step3: Solve for \(x\)

Divide both sides of the equation \(14x^{2}=350\) by \(14\): \(x^{2}=\frac{350}{14} = 25\). Take the square root of both sides. Since \(x>0\) (as it represents a dimension), \(x = 5\).

Step4: Find length and width

Length \(l=7x\), substitute \(x = 5\), so \(l=7\times5=35\) meters. Width \(w=2x\), substitute \(x = 5\), so \(w=2\times5 = 10\) meters.

Answer:

length = \(35\) meters, width = \(10\) meters