Question

If the length of a building is 2 1 2 times the width and each dimension is increased by 7 ft, then the perimeter is 266 ft. Find the dimensions of the original building in ft.

Answer 1

The original dimensions of the building is 95 ft × 38 ft.

Step-by-step explanation:

Let the original length be 'l' and original width be 'w'.

Given:

Original length (l) =
`2(1)/(2)* original\ width`

Original width = 'w'.

So,
`l=2(1)/(2)w=(5)/(2)w`

Now, as per question:

Length and width is increased by 7 ft.

So, new length (l') =
`l+7=(5w)/(2)+7`

New width (w') =
`w+7`

New perimeter (P) = 266 ft

Perimeter is given as:

`P=2(l' +w')\\\\266=2((5w)/(2)+w)\\\\(266)/(2)=(5w+2w)/(2)\\\\266=7w\\\\w=(266)/(7)=38\ ft`

Therefore, original width = 38 ft.

Original length is,
`l=(5* 38)/(2)=(190)/(2)=95\ ft`

Hence, the original dimensions of the building is 95 ft × 38 ft.