Respuesta :
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 (= [tex]\frac{15}{2}[/tex]) feet = [tex]\frac{15}{2}[/tex]×12 = 90 inches
∴ we get
The dimensions of the actual garden is 60 inches by 90 inches.
1.)
As,
[tex]\frac{60}{3} = \frac{20}{1} = 20 : 1[/tex]
[tex]\frac{90}{4.5} = \frac{900}{45} =\frac{20}{1} = 20 : 1[/tex]
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×[tex]\frac{5}{2}[/tex] inches by [tex]4.5 (\frac{5}{2})[/tex] 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 = [tex]\frac{60}{7.5}[/tex] = [tex]\frac{600}{75} = \frac{8}{1} = 8 : 1[/tex]
