Question

A billboard is 2.5 times as long as it is wide.The area of the billboard is 2,250 ft.A scale drawing is made of the billboard,and the area of the scale drawing is 160 in.What is the scale used in the scale drawing?(Explain)

Answer 1

Answer:

1 inch : 14.08 feet

Step-by-step explanation:

First we need to find to find the length and the width of the billboard.

The area of a rectangle is given by A= length x width

Let's call w the width of the billboard ⇒The length of the billboard will be 2.5w

Area = w (2.5w)

2,250 = 2.5w²

2250/2.5 = w²

900 = w²

30 = w

Now, to find the scale in the drawing we are going to use a ratio.

• We have the width of the billboard, the area of the billboard and the area of the scale drawing.
• We are going to write these values as a ratio to find the width of the scale drawing.

$\frac{x}{30} =\frac{160}{2250}\\ x=\frac{(160)(30)}{2250} \\x= 2.13$

Therefore, the width of the scale drawing is 2.13.

To find the scale used we can use a rule of three:

2.13 inches ------- 30 feet

1 inches --------------  x feet

x = 30/2.13 = 14.08 feet

Therefore, the scale used is 1 inch: 14.08 feet

Answer 2

Width = w
Length = 2.5w

Area of Rectangle: Width × Length
w (2.5w) = 2250
2.5w^2 = 2250
w^2 = 2250/2.5 = 900
w = Sq rt of 900 = 30
l = 75

Ratio of inches to ft
x/30 = 160/2250
cross multiply: 2250x = 160 × 30
2250x = 4800
x = 4800/2250 = 2.13333...

length
x/75=160/2250
2250x = 75(160)
2250x = 12,000
x= 12,000/2250
x = 5.3333...

scale is 2.13" × 5.33"