Question

Penny’s backyard contains a flower garden. The dimensions of the actual garden are 5 feet by 7½ feet. A scale drawing of the flower garden is shown below.
1. What is the scale factor from the actual flower garden to the scale drawing?

Be sure to express your ratio in simplest form.




2. If the drawing is enlarged by a scale factor of 5/2, what would be the dimensions of the flower garden in the new scale drawing? Express your dimensions in decimal form. Enter the smaller of your two lengths in the first answer box.


inches x

inches


3. What is the scale factor from the actual flower garden to the new scale drawing?

Be sure to express your ratio in simplest form.

Answer 1

Answer:

1.) Scale factor from the actual flower garden to the scale drawing = 20 : 1

2.) Dimensions of the flower garden in the new scale drawing = 7.5 inches × 11.25 inches

3.) Scale factor from the actual flower garden to the new scale drawing = 8:1

Step-by-step explanation:

Given - Penny’s backyard contains a flower garden. The dimensions of the

             actual garden are 5 feet by 7½ feet. A scale drawing of the flower

             garden is 3 inches by 4.5 inches.

To find - 1. What is the scale factor from the actual flower garden to the

                  scale drawing?

              2. If the drawing is enlarged by a scale factor of 5/2, what would    

                  be the dimensions of the flower garden in the new scale

                  drawing?

              3. What is the scale factor from the actual flower garden to the

                   new scale drawing?

Proof -

As we know that,

1 feet = 12 inches

⇒5 feet  = 5×12 = 60 inches

  7½ (= $\frac{15}{2}$) feet = $\frac{15}{2}$×12 = 90 inches

∴ we get

The dimensions of the actual garden is 60 inches by 90 inches.

1.)

As,

$\frac{60}{3} = \frac{20}{1} = 20 : 1$

$\frac{90}{4.5} = \frac{900}{45} =\frac{20}{1} = 20 : 1$

So,

Scale factor from the actual flower garden to the scale drawing = 20 : 1

2.)

As given,  If the drawing is enlarged by a scale factor of 5/2

⇒Dimensions of flower garden = 3×$\frac{5}{2}$ inches by $4.5 (\frac{5}{2})$ inches

                                                    = 7.5 inches by 11.25 inches

∴ we get

Dimensions of the flower garden in the new scale drawing = 7.5 inches × 11.25 inches

3.)

Scale factor from the actual flower garden to the new scale drawing = $\frac{60}{7.5}$ = $\frac{600}{75} = \frac{8}{1} = 8 : 1$