# 4.04 Lengths of similar figures

Worksheet
Lengths of Similar figures
1

A rectangle is 8\text{ cm} long and 6\text{ cm} wide. If its dimensions are enlarged such that the length is now 28\text{ cm} , find the new width.

2

A square with 2\text{ cm} sides is enlarged by 500\%. How long are the sides on the new square?

3

An equilateral triangle of side length 6\text{ cm} is to be enlarged by a factor of 5.

a

What will be the side length of the resulting triangle?

b

What will be the size of each angle in the resulting triangle?

4

For the similar figures given, the scale factor used to enlarge the smaller quadrilateral is 4.5.

Find the length of FG.

5

The dimensions of the triangle shown are enlarged using a scale factor of 3.1.

Find the new length of:

a

AB

b

BC

c

CA

6

The dimensions of the triangle shown are reduced using a scale factor of 0.92.

Find the new length of:

a

AB

b

BC

c

CA

7

Consider the following similar triangles:

a

Find the enlargement factor.

b

Find the value of x.

8

Consider the following similar triangles:

a

Find the reduction factor.

b

Find the value of m.

Applications
9

A school building reaching h metres high casts a shadow of 30 \text{ m} while a 3 \text{ m} high tree casts a shadow of 6 \text{ m} . Solve for h.

10

A 1.1\text{ m} high fence casts a shadow of length 1.5\text{ m} . At the same time, a lamp post of height 3.9 metres casts a shadow of length L metres. Find the value of L, rounding to one decimal place.

11

A stick of height 1.1\text{ m} casts a shadow of length 2.2\text{ m}. At the same time, a tree casts a shadow of 6.2\text{ m}. If the tree has a height of h metres, solve for h.

12

A 4.9\text{ m} flagpole casts a shadow of 8.6\text{ m} . Amelia casts a shadow of 2.5\text{ m}. If Amelia is h metres tall, solve for h correct to one decimal place.

13

James is 1.7\text{ m} tall and casts a shadow 2\text{ m} long. At the same time, a tower casts a shadow 13\text{ m} long. If the tower is h metres high, solve for h correct to one decimal place.

14

A boy wants to measure his height. He stands in the sun and takes note of where his shadow ends and places a 76 cm pole vertically in the ground at the end of his shadow. He then measures the height and length of the stick's shadow.

Find the height of the boy.

15

A large tree casts a shadow of 32 m. At the same time, a 1.2 m high fence post, standing vertically, casts a shadow of 4.5 m. Find h, the height of the tree in metres. Round your answer to two decimal places.

16

A fireman's ladder reaches 12.3\text{ m} up a building. The ladder is propped up by a support, placed 5.3\text{ m} from the building and 3.3\text{ m} from the base of the ladder. If the support is L metres long, solve for L. Round your answer to one decimal place.

17

Two similar triangles are created by cables supporting a yacht's mast.

Find the height of the mast:

18

A surveyor needs to measure the distance across a river. There are two trees on the opposite bank that are 34 m apart. She stands 5 m from the bank, directly opposite the first tree. Her assistant has to move 7.7 m along the bank to place a stick directly in her line of sight to the second tree. Find the width d of the river correct to the nearest metres.

19

Engineers want to determine the distance for a bridge to be built between points A and B. The diagram is an aerial view of their measurements. Point C is chosen so that AC is perpendicular to AB, and point E is chosen so that DE is perpendicular to AC.

The following measurements are taken: CA = 332 metres, CD = 103 metres and DE = 119 metres.

Find the distance AB to the nearest metre.

20

James stands at point A, as shown in the adjacent figure, so that he is in line with the pier and the tree on the other side of the canal. He then measures the direct distance to the edge of the water to be 14 m, and the distance along the canal to be 25 m as shown. The distance of the tree from the jetty is known to be 137 m. If the width of the canal is w metres, solve for w. Round your answer to the nearest metre.