Similar Triangles — Practice

Question 1

Fill in the blanks with 'similar' or 'not similar', with a reason: (a) All squares are ...  (b) All isosceles triangles are ...

Accepted Answer

(a) similar;  (b) not similar

Question 2

In triangle PQR, E and F are points on PQ and PR. If PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm, state whether EF is parallel to QR.

Accepted Answer

No, EF is not parallel to QR

Question 3

In triangle ABC, DE is parallel to BC with AD/DB = 3/5 and AC = 5.6 cm. Find AE.

Accepted Answer

AE = 2.1 cm

Question 4

In the figure LM is parallel to AB, with AL = x - 3, AC = 2x, BM = x - 2 and BC = 2x + 3. Find x.

Accepted Answer

x = 9

Question 5

In the given figure angle ADE = angle CBA, AD = 3.8 cm, AE = 3.6 cm, BE = 2.1 cm and BC = 4.2 cm. Find DE.

Accepted Answer

DE = 2.8 cm

Question 6

The perimeters of two similar triangles are 30 cm and 20 cm. If one side of the first triangle is 12 cm, find the corresponding side of the second.

Accepted Answer

8 cm

Question 7

A girl of height 90 cm is walking away from the base of a lamp post at 1.2 m per second. If the lamp post is 3.6 m above the ground, find the length of her shadow after 4 seconds.

Accepted Answer

1.6 m

Question 8

A flag pole 4 m tall casts a 6 m shadow. At the same time a nearby building casts a shadow of 24 m. How tall is the building?

Accepted Answer

16 m

Question 9

In the given figure AB, CD and EF are all parallel, with AB = 7.5 cm, EF = 4.5 cm and CF = 3 cm. Find DC and BC.

Accepted Answer

DC = 2.8125 cm and BC = 5 cm

Question 10

D, E and F are the midpoints of the sides BC, CA and AB of triangle ABC. Find the ratio of the areas of triangle DEF and triangle ABC.

Accepted Answer

1 : 4

Question 11

In triangle ABC, XY is parallel to AC and XY divides the triangle into two parts of equal area. Find AX/XB.

Accepted Answer

(root2 - 1) : 1

Question 12

Triangle ABC is similar to triangle DEF, with BC = 3 cm, EF = 4 cm and area of triangle ABC = 54 square cm. Find the area of triangle DEF.

Accepted Answer

96 square cm

Question 13

The areas of two similar triangles are 81 square cm and 49 square cm. If the altitude of the bigger triangle is 4.5 cm, find the corresponding altitude of the smaller one.

Accepted Answer

3.5 cm

Question 14

ABC is a triangle and PQ is a straight line meeting AB at P and AC at Q. If AP = 1 cm, BP = 3 cm, AQ = 1.5 cm and CQ = 4.5 cm, prove that the area of triangle APQ is one sixteenth of the area of triangle ABC.

Accepted Answer

Proved: the ratio of sides is 1 : 4, so the ratio of areas is 1 : 16

Question 15

A 24 m long wire is attached to a vertical pole of height 18 m, with a stake at the other end. How far from the base of the pole should the stake be driven so that the wire is taut?

Accepted Answer

6 root7 metres, about 15.87 m

Question 16

Two poles of heights 6 m and 11 m stand on level ground. If the distance between their feet is 12 m, find the distance between their tops.

Accepted Answer

13 m

Question 17

A ladder 15 m long reaches a window 9 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side to reach a window 12 m high. Find the width of the street.

Accepted Answer

21 m

Question 18

ABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of triangle ABE and triangle ACD.

Accepted Answer

1 : 2

Question 19

The hypotenuse of a right triangle is 6 m more than twice the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle.

Accepted Answer

10 m, 24 m and 26 m

Question 20

An aeroplane leaves an airport and flies due north at 1000 km/h. At the same time another leaves the same airport and flies due west at 1200 km/h. How far apart will the two planes be after one and a half hours?

Accepted Answer

1800 root(61) divided by... that is, 300 root61 km, about 2343.1 km

Question 21

Ravi is 1.82 m tall. From a tree's base he walked 12.20 m along the tree's shadow to a position where the end of his shadow exactly overlaps the end of the tree's shadow. He is now 6.10 m from the end of the shadow. How tall is the tree?

Accepted Answer

5.46 m

Practice — Similar Triangles

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