    Question

# A square lawn is bounded on three sides by a path of $4m$ wide. If the area of the path is $\frac{7}{8}$ that of the lawn, find the dimensions of the lawn.

Open in App
Solution

## Step 1. Finding the area of square lawn and path:Let the length of the side of the square lawn be $x\mathrm{m}$.The area of square lawn $=side×side={x}^{2}{\mathrm{m}}^{2}$The area of the path $=\left(x+8\right)×4+x×4+x×4$ $=8x+4x+32$ $=12x+32{m}^{2}$Step 2. Finding the dimensions of the lawn:Now, the area of the path is $\frac{7}{8}$ that of the lawn.$12x+32=\frac{7}{8}{x}^{2}\phantom{\rule{0ex}{0ex}}96x+256=7{x}^{2}\phantom{\rule{0ex}{0ex}}7{x}^{2}-96x-256=0\phantom{\rule{0ex}{0ex}}7{x}^{2}-112x+16x-256=0\phantom{\rule{0ex}{0ex}}7x\left(x-16\right)+16\left(x-16\right)=0\phantom{\rule{0ex}{0ex}}\left(7x+16\right)\left(x-16\right)=0\phantom{\rule{0ex}{0ex}}x=16m,-\frac{16}{7}m$But the length cannot be negative.Thus, the dimensions of the square lawn is $16m$.  Suggest Corrections  0      Similar questions  Explore more