Question

Find the length of a rectangle lot with a perimeter of 82 meters if the length is 7 meters more then the width?

Answer 1

24 meters

Explanation:

If the short side of the rectangle = s, then the long side would be s+7.

The total perimeter then would be the sum of all 4 sides, where the sids are equal in pairs, i.e.
Perimeter = s+(s+7)+s+(s+7) = 4s+14 = 82
Therefore 4s=82-14 = 68
so s=17
As this is the short side, the long side is s+7=17+7=24
The length of the rectangle, therefore, is 24 meters

Answer 2

The length of the rectangle lot is `color(red)(24)` meters.

Explanation:

To start, I'll set up an equation to help solve this...

`2l+2w=p`, meaning the length twice plus the width twice equals the perimeter. We can fill this in with the known values:

`2l+2(l-7)=82`

`w` can be replaced by `(l-7)` because the problem states that the width is `7` meters shorter than the length.

Distribute the `2` to the `(l-7)` to get:

`2l+2l-14=82`

And combine like terms to get:

`4l=96`

Finally divide both sides by `4` to finish with:

`l=24`, meaning the length is `color(red)(24)` meters.

I'll check my work by plugging this info back in to the original equation to see if it works:

`2l+2w=p`
`2l+2w=82`
`2(24)+2(24-7)=82`
`2(24)+2(17)=82`
`color(green)(48+34=82)`

The equation works, meaning the length is `24` m and the width is `17` m.