Question

a scale model of a roof has a base of 10 ft and a height of 8 ft. the actual roof has a base of 25 ft. what is the height of the actual roof?
a. 18 ft
b. 12 ft
c. 22 ft
d. 20 ft

an engineer designs two ramps inclined at the same angle. ramp a has a height of 6 ft and a length of 12 ft. ramp b has a height of 9 ft. what is the length of ramp b?
a. 14 ft
b. 20 ft
c. 18 ft
d. 16 ft

a street light casts a shadow 12 feet long. a person 5 feet tall casts a shadow 3 feet long. what is the height of the streetlight?
a. 15 feet
b. 20 feet
c. 18 feet
d. 25 feet

Explanation:

First Question (Scale Model of Roof)

Step1: Set up proportion

Let \( h \) be the height of actual roof. The ratio of base to height should be equal for model and actual. So \(\frac{10}{8}=\frac{25}{h}\)

Step2: Cross - multiply and solve

Cross - multiplying gives \( 10h = 8\times25 \). Then \( 10h=200 \), and dividing both sides by 10, \( h = 20 \)

Step1: Set up proportion

Since the ramps have the same angle, the ratio of height to length is equal. Let \( l \) be the length of Ramp B. So \(\frac{6}{12}=\frac{9}{l}\)

Step2: Cross - multiply and solve

Cross - multiplying gives \( 6l=12\times9 \). Then \( 6l = 108 \), and dividing both sides by 6, \( l = 18 \)

Step1: Set up proportion

Let \( H \) be the height of street light. The ratio of height to shadow length is equal for person and street light. So \(\frac{5}{3}=\frac{H}{12}\)

Step2: Cross - multiply and solve

Cross - multiplying gives \( 3H=5\times12 \). Then \( 3H = 60 \), and dividing both sides by 3, \( H = 20 \)

Answer:

d. 20 ft

Second Question (Ramps)