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)

Question

Mathematics

Petie

25 December, 16:40

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)

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Ariana Knox · Answer 1

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"