Chapter 7.6, Problem 20PPS

a.

To determine

Check whether the actual sign is a dilation of her sample.

Explanation of Solution

Given:

Aimee painted sample sign (shown in the diagram) using half bottle of glass paint. The actual sign dimension is $3$ feet by $7\frac{1}{2}$ feet.

  

Calculation:

For actual sign

  $\frac{3}{7\frac{1}{2}}=\frac{3}{\frac{15}{2}}=3\cdot \frac{2}{15}=\frac{2}{5}$

For sample

  $\frac{6}{15}=\frac{6\cdot \frac{1}{12}}{15\cdot \frac{1}{12}}=\frac{2}{5}$

Since $\frac{3\text{feet}}{7\frac{1}{2}\text{feet}}=\frac{6\text{in}\text{.}}{15\text{in}\text{.}}$

Hence theactual sign is a dilation of her sample.

b.

To determine

Find the number of bottles of paint required for the actual sign.

Answer to Problem 20PPS

Aimee will need $18$ bottles of paint.

Explanation of Solution

Given:

Aimee painted sample sign (shown in the diagram) using half bottle of glass paint. The actual sign dimension is $3$ feet by $7\frac{1}{2}$ feet.

  

Calculation:

Find the area of the sample.

Area of the sample

  $=6\text{in}\text{.}\cdot 15\text{in}\text{.}=6\cdot \frac{1}{12}\text{feet}\cdot 15\cdot \frac{1}{12}\text{feet}=0.625{\text{feet}}^2$

Area of actual sign

  $=3\text{feet}\cdot 7\frac{1}{2}\text{feet}=3\text{feet}\cdot \frac{15}{2}\text{feet}=22.5{\text{feet}}^2$

Now,

Aimee paints an area of $0.625{\text{feet}}^2$ with $\frac{1}{2}$ a bottle of paint.

Aimee paints an area of $22.5{\text{feet}}^2$  $=\frac{1}{2\cdot 0.625}\cdot 22.5=\frac{22.5}{1.25}=18$ bottles of paint.

HenceAimee will need $18$ bottles of paint.