Question

1. the figure below is a scale drawing of a garden. if the scale used is 1/4 inch = 3 feet, then what is the perimeter of the actual garden? 3 1/4 in 1/2 in perimeter: _

Explanation:

Step1: Find actual length and width

The scale is $\frac{1}{4}$ inch = 3 feet. The length of the scale - drawing is $3\frac{1}{4}$ inches and the width is $\frac{1}{2}$ inches.
For the length: Let the actual length be $L$. We have the proportion $\frac{\frac{1}{4}\text{ in}}{3\text{ ft}}=\frac{3\frac{1}{4}\text{ in}}{L}$. Cross - multiply: $\frac{1}{4}L = 3\times3\frac{1}{4}$. Since $3\frac{1}{4}=\frac{13}{4}$, then $\frac{1}{4}L=3\times\frac{13}{4}=\frac{39}{4}$, and $L = 39$ feet.
For the width: Let the actual width be $W$. We have the proportion $\frac{\frac{1}{4}\text{ in}}{3\text{ ft}}=\frac{\frac{1}{2}\text{ in}}{W}$. Cross - multiply: $\frac{1}{4}W=3\times\frac{1}{2}$, so $W = 6$ feet.

Step2: Calculate the perimeter

The formula for the perimeter of a rectangle is $P = 2(L + W)$. Substitute $L = 39$ feet and $W = 6$ feet into the formula: $P=2(39 + 6)=2\times45 = 90$ feet.

Answer:

90 feet