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In this lesson, we will learn how to calculate the scale factor and the lengths of both the scaled model and the actual one and to apply this to real-world problems.

Q1:

The distance between two cities on a map is 17 cm and the actual distance between them is 68 km. If the distance between two other cities on the same map is 15 cm, determine the real distance between them.

Q2:

Every inch in a scale model of a car represents 1 2 ft in reality. If a vehicle is 4 1 2 ft long, how long is the scale model?

Q3:

A magnified picture of an insect was taken with an enlargement ratio of 3 1 0 1 : . Determine the actual length of the insect if the insect’s length in the picture is 3.1 cm.

Q4:

A scale model of a building is 4.8 inches tall. If 2 inches on the model scale up to 25 feet in reality, determine the actual height of the building.

Q5:

A model of a tree is made using a scale of 1 ∶ 3 0 i n f t . Find the height of the actual tree if the height of the model is 2 2 3 in.

Q6:

Bassem drew a map of his school using a scale of 1 inch for every 10 ft. Determine the distance with which the 800 feet between the playground and the boys restroom would be represented on the map.

Q7:

Determine the actual area of the given square which is drawn to a scale of 1 cm = 4 km.

Q8:

Given that the distance between two cities on a map is 4.4 cm and the actual distance between them is 26.4 km, what is the drawing scale of the map?

Q9:

Complete the table.

Q10:

A map is scaled such that every 1 8 in is equivalent to 50 mi. How many miles are represented by 4 inches on the map?

Q11:

Q12:

Consider the given figure.

State whether the following is true or false: There is a similarity transformation that would map circle 𝐴 to a position which makes it concentric with circle 𝐵 .

What scale factor would dilate circle 𝐴 to circle 𝐵 ?

Q13:

A picture with width 13 mm and height 37 mm is magnified so that its width becomes 3.25 cm and height becomes 𝑋 cm. Find the value of 𝑋 .

Q14:

At a scary movie opening, a cardboard model of the monster was 9 inches tall. In the movie, the monster’s actual height was 53 feet. What was the scale of the model?

Q15:

Find the scale factor of the smaller parallelogram to the bigger one in the given figure.

Q16:

Determine the area of the given rectangle which is drawn to a scale of 1 in = 5 ft.

Q17:

A polygon has area 136. If the area is doubled, by what factor is each side increased?

Q18:

A photograph 18 inches by 33 inches was enlarged into a poster size picture with a scale factor of 3 4 : . Determine the dimensions of the poster.

Q19:

The figure below shows a drawing of the floor plan of a house. The drawing scale is 1 ∶ 1 0 0 . What is the length and width of the real-life living room?

Q20:

An insect’s body is 9 centimeters long with 21-centimeter legs. Determine the length of its legs in a model where its body is 3 meters long.

Q21:

The table below shows some information about a scale drawing. Complete the missing details, including whether the drawing is a magnification or reduction from real life.

Q22:

Given a scale drawing, which of the following is equal to the scale?

Q23:

A map is drawn with a drawing scale of 1 ∶ 3 8 0 0 0 0 0 . If the actual distance between two cities is 76 km, determine the distance between them on the map.

Q24:

A rectangular picture with width 20 mm and height 61 mm is magnified to 4 cm by 12.2 cm. What is the magnification ratio?

Q25:

Nabil is drawing a map to a scale of . If the distance between two cities on the map is 4.5 cm, find the actual distance between them in kilometres.

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