Question

1. the figure below is a scale drawing of a garden. if the scale used is $\frac{1}{4}$ inch = 3 feet, then what is the perimeter of the actual garden? $\frac{1}{2}$ in $1\frac{3}{4}$ in

Explanation:

Step1: Calculate the actual length of the rectangle

The scale is \(\frac{1}{4}\) inch \( = 3\) feet.
For the length of \(1\frac{3}{4}=\frac{7}{4}\) inches.
Let \(x\) be the actual length.
Set up a proportion: \(\frac{\frac{1}{4}}{3}=\frac{\frac{7}{4}}{x}\)
Cross - multiply: \(\frac{1}{4}x = 3\times\frac{7}{4}\)
Solve for \(x\): \(x = 21\) feet.

Step2: Calculate the actual width of the rectangle

For the width of \(\frac{1}{2}\) inches.
Let \(y\) be the actual width.
Set up a proportion: \(\frac{\frac{1}{4}}{3}=\frac{\frac{1}{2}}{y}\)
Cross - multiply: \(\frac{1}{4}y=3\times\frac{1}{2}\)
Solve for \(y\): \(y = 6\) feet.

Step3: Calculate the perimeter of the rectangle

The formula for the perimeter of a rectangle is \(P = 2(l + w)\)
Substitute \(l = 21\) feet and \(w = 6\) feet.
\(P=2(21 + 6)=2\times27 = 54\) feet.

Answer:

\(54\) feet