Question

a rectangle with an area of 360 square millimeters has a length and width in a ratio of 5:2. what are the length and width? length = millimeters width = millimeters

Explanation:

Step1: Set up variables

Let the length be \(5x\) millimeters and the width be \(2x\) millimeters. The area formula for a rectangle is \(A = length\times width\). So, \(A=(5x)\times(2x)\).

Step2: Solve for \(x\)

Since \(A = 360\) square - millimeters, we have the equation \((5x)\times(2x)=360\). Simplify the left - hand side: \(10x^{2}=360\). Divide both sides by \(10\): \(x^{2}=\frac{360}{10}=36\). Take the square root of both sides: \(x = 6\) (we take the positive value since \(x\) represents a length).

Step3: Find length and width

Length \(l = 5x\), substitute \(x = 6\), so \(l=5\times6 = 30\) millimeters. Width \(w = 2x\), substitute \(x = 6\), so \(w=2\times6=12\) millimeters.

Answer:

length = \(30\) millimeters, width = \(12\) millimeters