Triangles — Chapter Test | Class 10 IMO

Q1

A rectangular plot 40 m by 30 m is crossed by a diagonal path. The path length is:

√(40² + 30²) = √2500 = 50 m.

Q2

A triangle with sides 9, 12 and 15 cm is:

9² + 12² = 81 + 144 = 225 = 15², so it is right-angled.

Q3

If two triangles have all three pairs of sides proportional, they are similar by:

Three proportional sides give SSS similarity.

Q4

In △ABC, DE ∥ BC. If AD/DB = 2/3 and AE = 4 cm, then EC equals:

AE/EC = 2/3 gives 4/EC = 2/3, so EC = 6 cm.

Q5

For two similar triangles, the ratio of their perimeters equals the ratio of their:

Perimeters scale in the same ratio as corresponding sides.

Q6

A line drawn parallel to the base of a triangle cuts off a smaller triangle that is:

The smaller triangle has the same angles as the original, so it is similar.

Q7

A right triangle has legs 6 cm and 8 cm. Its hypotenuse is:

√(6² + 8²) = √100 = 10 cm.

Q8

A ladder 13 m long rests against a wall, reaching 12 m up. Its foot is from the wall:

√(13² − 12²) = √25 = 5 m.

Q9

If two triangles are similar and also equal in area, then they are:

Equal areas force the scale factor to be 1, so the triangles are congruent.

Q10

In a right triangle ABC right-angled at B, with AB = 6 cm and BC = 8 cm, the altitude BD from B to the hypotenuse AC has length:

AC = 10 cm, and BD = (AB × BC)/AC = 48/10 = 4.8 cm.

Q11

In △ABC, DE ∥ BC with AD = 1.5 cm, DB = 3 cm and AE = 1 cm. Then EC equals:

AD/DB = AE/EC gives 1.5/3 = 1/EC, so EC = 2 cm.

Q12

Pythagoras' theorem applies only to:

The relation hypotenuse² = sum of squares holds only for right triangles.

Q13

The area of an equilateral triangle of side 6 cm is:

Area = (√3/4)·6² = (√3/4)·36 = 9√3 cm².

Q14

A wheelchair ramp rises 3 m over a horizontal run of 4 m. The length of the ramp is:

√(3² + 4²) = √25 = 5 m.

Q15

In a right triangle, the altitude drawn to the hypotenuse creates two smaller triangles that are:

Each smaller triangle is similar to the whole triangle (and to each other).