Finding length and width using ratio and area

Question

The area of the rectangle is 300 in². The ratio of the length to the width is 4 : 3. Find the length and the width.

Answer 1

Let L be the length and W be the width of the rectangle.

Then since the ratio of L to W is 4 to 3,

LlW = 4/ 3, since ratios are just another way of writing a fraction.

So L= 4W/ 3 , by isolating L.

Since the area of a rectangle is length multiplied by width,

L x W= 300 in² . We can now substitute for L.

4W/3 x W = 300.

or, 4 W²/ 3 = 300. Multiply both sides by 3.

4 W² = 900 Divide both sides by 4.

W² = 900 /4 Take the square root of both sides.

W = 30/2

= 15in

Going back to our initial ratio,

L = 4W/3. Substitute for our value of W.

= 4(15) /3

= 20 in.

Check your answer: 15 x 20 = 300.