Finding the dimensions

Question

The length of a rectangle is 11 meters less than three times its width. Its area is 364 square meters. What are the dimensions of the rectangle?

Answer 1

Hi Elisa,

The area of a rectangle is A = Length * width.

The problem mentions a relationship between the length and the width: 11 less 3 times the width.

That means L = 3*W -11.

You then substitute L by 3*W - 11 in the area formula, which gets you: A = (3w-11)(w)

Multiplication gets you: A = 3w² - 11w

Replace A by 364 because that is the area given to you and you have 364 = 3w² - 11w.

Subtract 364 on both sides and you get a quadratic equation: 3w² - 11w - 364 = 0

From there, you can use the quadratic formula, which will give you two possible solutions for the width.

Choose the one that makes the most sense (it'll be clear to you. Hint: sides of a rectangle can only be positive).

Once you choose the logical solution for the width, go back to the relationship between length and width, then plug that solution where W is. You will get the length. Problem solved.

Cheers!