Find the perimeter of the original rectangle.

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Question from Hannah, a student:

The area of a rectangle is 360 square meters. If the rectangle's length is increased by 10 meters and the width is decreased by 6 meters, its area does not change. Find the perimeter of the original rectangle.

Hannah,

In order to answer this question, we need to know what it is looking for. This is usually in the last sentence.

"Find the perimeter of the original rectangle."

We also need to know what information is given,

Area = 360m²
Length increased by 10,...width decreased by 6,...area is the same.

Now, what do we already know that will help to solve this problem (specifically about area, perimeter, and length and width)?

Area = Length * Width
Perimeter = 2*Length + 2*Width

Now we need to use variables (letters) to represent length and width,

Let x = length
Let y = width
So,
x * y = Area = 360,
2x + 2y = Perimeter

Lastly, we have to make our own statement from the question to solve this problem,

Length increased by 10,...width decreased by 6,...area is the same
(x + 10) * (y - 6) = 360

If we combine what we know about area,

Area = 360
360 = (x + 10)*(y - 6)
360 = x * y

We will be able to solve for Perimeter.

Always start with what you know!
Melanie

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.