Question

1. a rectangular garden measures 10 meters by 6 meters. you plan to create a scale - drawing of the garden using a scale factor of 1.5. what will be the area of the scale drawing? 5. a square tile has a side length of 12 inches. a scale drawing of the tile is made using a scale factor of ⅓. what is the area of the scale drawing?

Explanation:

4.

Step1: Find the new length and width

When using a scale - factor of \(k = 1.5\), the new length \(l_{new}\) and width \(w_{new}\) of the rectangle are found by dividing the actual length and width by the scale - factor. The actual length \(l = 10\) meters and width \(w = 6\) meters. So, \(l_{new}=\frac{10}{1.5}=\frac{100}{15}=\frac{20}{3}\) meters and \(w_{new}=\frac{6}{1.5}=4\) meters.

Step2: Calculate the area of the scale - drawing

The area of a rectangle \(A=l\times w\). So, \(A = l_{new}\times w_{new}=\frac{20}{3}\times4=\frac{80}{3}\approx26.67\) square meters.

Step1: Find the new side - length

The scale - factor \(k=\frac{1}{4}\). The actual side - length of the square tile \(s = 12\) inches. The new side - length \(s_{new}=s\times k=12\times\frac{1}{4}=3\) inches.

Step2: Calculate the area of the scale - drawing

The area of a square \(A = s^{2}\). So, \(A=s_{new}^{2}=3^{2}=9\) square inches.

Answer:

\(\frac{80}{3}\text{ square meters}\)

5.