Question

A rectangular rink having dimensions 30 m by 50 m is to be expanded by adding rectangular strips of equal width to one length and one width. If the new rink will have an area of 1749 m2, what will be the width of the strip?

Answer 1

3 meters.

Explanation:

Please find the attachment.

Let x represent the strip added to one length and one width.

We have been given that a rectangular rink having dimensions 30 m by 50 m is to be expanded by adding rectangular strips of equal width to one length and one width. So new dimensions of rink would be
`(30+x)` and
`(50+x)`.

We have been given that area of the new rink is 1749 square meters. We know that area of rectangle is length times width, so we can represent this information in an equation as:

`(30+x)(50+x)=1749`

`1500+30x+50x+x^2=1749`

`x^2+80x+1500=1749`

`x^2+80x+1500-1749=1749-1749`

`x^2+80x-249=0`

`x^2+83-3x-249=0`

`x(x+83)-3(x+83)=0`

`(x+83)(x-3)=0`

Using zero product property, we will get:

`(x+83)=0,(x-3)=0`

`x=-83,x=3`

Since length cannot be negative, therefore, width of the strip is 3 meters.