Answer:
The original dimensions of the building is 95 ft × 38 ft.
Explanation:
Let the original length be 'l' and original width be 'w'.
Given:
Original length (l) = [tex]2\frac{1}{2}\times original\ width[/tex]
Original width = 'w'.
So, [tex]l=2\frac{1}{2}w=\frac{5}{2}w[/tex]
Now, as per question:
Length and width is increased by 7 ft.
So, new length (l') = [tex]l+7=\frac{5w}{2}+7[/tex]
New width (w') = [tex]w+7[/tex]
New perimeter (P) = 266 ft
Perimeter is given as:
[tex]P=2(l' +w')\\\\266=2(\frac{5w}{2}+w)\\\\\frac{266}{2}=\frac{5w+2w}{2}\\\\266=7w\\\\w=\frac{266}{7}=38\ ft[/tex]
Therefore, original width = 38 ft.
Original length is, [tex]l=\frac{5\times 38}{2}=\frac{190}{2}=95\ ft[/tex]
Hence, the original dimensions of the building is 95 ft × 38 ft.
