Review - Similarity and Scale Factor

The ratio of sunny days to cloudy days recently has been 2:5. If this pattern continues, how many sunny days would there be in 28 days?

• 4

• 8

• 20

• 11.2

Answer explanation

You can use: 2x + 5x = 28 to get the scale factor, and then multiply by 2....
or use

$\frac{2\ sunny}{7\ total}=\frac{x}{28\ total}$

What 2 things must be true in order for 2 figures to be similar?  

• their corresponding angles are equal

• their corresponding sides are proportional

• the angles in one figure are all the same 

• the sides are equal 

A map has a scale of 1 inch: 125 feet. How many actual feet does 4 inches represent on the map?

• 500 ft

• 31.25 ft

• 250 ft

Answer explanation

$\frac{1\ in\ }{125\ ft}=\frac{4\ in}{x}$

The perimeter of a polygon is 90 inches. If a scale factor of 2.5 is used to increase the size of the polygon, what is the new perimeter?

• 225 in.

• 36 in

• 500 in.

Answer explanation

$P_1\ \cdot\ SF\ =\ P_2$

$90\ \cdot\ \left(2.5\right)\ =\ new\ perimeter$

The ratio of measures of the sides of a quadrilateral are

4 : 6 : 8 : 10 and its perimeter is 168 feet. Find the length of the longest side of the quadrilateral?

• 6 ft

• 60 ft

• 28 ft

• 40 ft

Answer explanation

4x + 6x + 8x + 10x = 168

x = 6 (which is the scale factor)

... so the longest side will be 10(6)

The scale on a map indicates that 1.5 cm represents 200 miles. If the distance on the map between 2 cities measures 2.4 cm, how many miles apart are the cities?

• 320 miles

• 18 miles

• 55.6 miles

• 480 miles

Answer explanation

$\frac{cm}{miles}=\frac{1.5\ cm}{200\ mi\ }=\frac{2.4\ cm}{x}$

A replica of The Thinker is 8 inches tall.

An actual statue of The Thinker, is 10 feet tall.

If the replica is 3.2 inches wide at the base, how wide is the actual statue?

• 4 ft

• 25 ft

• 100 ft

• 40 ft

Answer explanation

$\frac{tall}{wide}=\ \frac{8\ in}{3.2\ in}=\ \frac{10ft}{x}$

or
$\frac{replica}{actual}=\frac{8\ in}{10\ ft}=\frac{3.2\ in}{x}$

A cable that is 42 feet long is divided into lengths in the ratio of 3:4. What is the length of the larger piece after it is divided?

• 24 ft

• 18 ft

• 6 ft

• 31.5 ft

Answer explanation

$\frac{long\ part}{total}=\frac{4}{7}=\frac{x}{42}$
or

3x + 4x = 42 ...

x = 6 (is the scale factor),

then multiply by larger part

The ratio of men to women at a class 

is 6 to 5. 

How many women students are there if there are 3630 total people?

• 1650

• 1980

• 1375

• 330

Answer explanation

$\frac{women}{total}=\frac{5}{11}=\frac{x}{3630}$
or
$6x\ +\ 5x\ =\ 3630$
$x\ =\ 330$ this is the scale factor, then multiply by 5 (for the women)

A spotlight is placed on the ground 30 feet from the wall of a building. A 6 foot tall person stands 8 feet from the light source, between it and the wall. A shadow is cast on the wall. How tall is the shadow on the wall?

• 22.5 ft

• 16.5 ft

• 22 ft

• 15 ft

Answer explanation

$\frac{tall}{shadow}=\frac{6\ ft}{8ft}=\frac{y}{30\ ft}$