Question

The area of a gymnasium is 956 yd2. The width of the gymnasium is 4 yd longer than its length. Find the length and width of the gymnasium (round to the nearest yard). Include a labeled diagram in your work for full credit?

Answer 1

L = 29

w = 33

Explanation:

Area = w × L

= (L + 4) × L

⇔ 956 = L² + 4L

⇔ 956 = (L + 2)² − 4

⇔ 956 + 4 = (L + 2)²

⇔ 960 = (L + 2)²

`\Leftrightarrow L+2=√(960)`

`\Leftrightarrow L+2=30.983866769659`

`\Longrightarrow L+2 \approx 31`

`\Longrightarrow L \approx 29`

`\Longrightarrow w=L+4 \approx 29+4\approx33`