Geometry Ratios and Proportions

A model of a lighthouse has diameter 8 inches and height 18 inches. If the actual diameter of the lighthouse is 20 feet, find its actual height.

• 30 ft

• 35 ft

• 45 ft

• 50 ft

A scale drawing of a billboard uses the scale 4 cm:9 ft. The length of the billboard in the drawing is 11 cm. How long is the actual billboard?

• 13 ft

• 20.75 ft

• 24.75 ft

• 22 ft

A triangle’s angle measures are in the extended ratio of 2 : 4 : 9. Find the measures of the angles.

• 20^o, 40^o, 90^o

• 24^o, 48^o, 108^o

• 24^o, 32^o, 124^o

• 20^o, 40^o, 100^o

Answer explanation

Using the ratio

first angle = 2x°

2nd angle = 4x°

3rd angle = 9x°

Using triangle sum theorem find the value of x

2x + 4x + 9x = 180

once you have the value of x sub in for the angle expressions.

Answer explanation

Use cross products

4(n + 9) = 8n now solve for n.

Answer explanation

Use Cross Products

4(n + 2) = 5(n - 1) solve for n

What is it called when you set two ratios equal to each other?

• Proportion

• Fraction

• Ratio

• Congruent

The ratio of the sides of a rectangle is 3 to 5.

If the perimeter of the figure is 80 inches,

the shorter side is​ (a)   inches and the longer side is ​ (b)   inches

• 15

• 25

• 30

• 50

• 12

• 28

Answer explanation

Draw a rectangle and label the shorter side 3x and the longer side 5x.

Use perimeter equal to 80.

The pair of figures is similar. Find the missing side.

• x = 1

• x = 3

• x = 9

• x = 5

Are the triangles similar?

• Yes

• No

Review the picture.  Find the missing side measurement in the picture using a proportion.

• w = 18 m

• w = 6 m

• 6 m

• w = 0.16 m