Question

1. myra painted a picture of her dog, grover, using a scale factor of 15%. here is a picture of grover. how long is he in real life? image of a dog with a length measurement arrow 9. the picture on the right is a scale diagram of the picture on the left. find the unknown measurements, x and y. left figure: a pentagon with side 50, side 45, and base y; right figure: a smaller pentagon with side 20, side x, and base 24 10. vikram is drawing a scale diagram for the floor plan of his house, which has a width of 30 ft and a length of 90 ft. determine an appropriate scale he could use to fit his floor plan on a piece of paper that is 12 inches by 25 inches.

Explanation:

(Problem 8):

Step1: Note missing measured length

The length of the drawn dog is not provided in the image, so we define the drawn length as $L_{drawn}$. The scale factor is 15% = 0.15, meaning $L_{drawn} = 0.15 \times L_{real}$.

Step2: Solve for real length

Rearrange the scale factor formula to isolate the real length.
$L_{real} = \frac{L_{drawn}}{0.15}$

(Problem 9):

Step1: Calculate scale factor

Find the ratio of corresponding sides.
$\text{Scale factor} = \frac{20}{50} = 0.4$

Step2: Solve for $x$

Multiply the original side by the scale factor.
$x = 45 \times 0.4 = 18$

Step3: Solve for $y$

Rearrange the scale factor formula to find the original side.
$y = \frac{24}{0.4} = 60$

(Problem 10):

Step1: Convert feet to inches

1 ft = 12 inches, so convert house dimensions:
Width: $30 \times 12 = 360$ inches
Length: $90 \times 12 = 1080$ inches

Step2: Calculate width scale ratio

Find the ratio of paper width to house width.
$\frac{12}{360} = \frac{1}{30}$

Step3: Calculate length scale ratio

Find the ratio of paper length to house length.
$\frac{25}{1080} \approx \frac{1}{43.2}$

Step4: Choose the smaller scale

Select the more restrictive scale to fit both dimensions.
Use the scale $\frac{1}{45}$ (or 1 inch = 45 inches = 3.75 ft, a practical rounded scale that fits both)

Answer:

1. Let the measured length of the drawn dog be $L_{drawn}$. The real length is $\boldsymbol{\frac{L_{drawn}}{0.15}}$ (units match the drawn length's units).
2. $\boldsymbol{x=18}$, $\boldsymbol{y=60}$
3. An appropriate scale is $\boldsymbol{1:45}$ (1 inch on paper = 45 inches, or 3.75 feet, in real life; other slightly smaller scales like 1:40 also work, but 1:45 ensures a safe fit)