Olympiad – Class X – Mathematics - Triangles

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Question - 1

In the figure, \(\angle\)ABC=\(\angle\)DAC=90°, BC = 3 cm, AD = 2 cm and AB = 1 cm.What is the measure of AC + CD?

  • A \(\sqrt{2}(\sqrt{5}+\sqrt{7})cm\)
  • B \(\sqrt{5}(\sqrt{2}+\sqrt{7})cm\)
  • C \(\sqrt{2}(\sqrt{7}+\sqrt{5})cm\)
  • D \(\sqrt{7}(\sqrt{2}+\sqrt{2})cm\)

Question - 2

A paper is cut in the following shape

Which of the following is the correct statement?

  • A AE2= AD2 + ED2
  • B AC2 = AD2 + DE2
  • C AC2 = AB2+ AD2
  • D AE2= AB2+ BC2

Question - 3

In the given figure, what is the value of 'x' if AB IICD?

  • A 2 units
  • B 4 units
  • C 3 units
  • D 5 units

Question - 4

In \(\triangle\) ABC, DE|| BCand \({AD\over DB}={3\over5}.\) What is the length of AE if AC = 4.8 cm?

  • A 1.4 cm
  • B 1.8 cm
  • C 2.2 cm
  • D 3.6 cm

Question - 5

ABCD is a parallelogram in which EF is drawn parallel to BC such that
AE = (4x - 3) cm, AF = (8x - 7) cm, BE= (3x - 1) cm and CF = (5x - 3) cm.

What is the value of 'x'?

  • A 1
  • B -1
  • C -5
  • D \({-1\over2}\)

Question - 6

In \(\triangle\) ABC, if \({AD\over DB}={AE\over EC},\) and \(\angle\) ADE =\(\angle\) ACB, what type of triangle is \(\triangle\)ABC?

  • A Right triangle
  • B Acute angled triangle
  • C Isosceles triangle
  • D Obtuse angled triangle

Question - 7

The altitudes of two similar triangles are 4 cm and 6 cm. If the area of one triangle is 36 cm2, what is the area of the other?

  • A 16 cm2
  • B 36 cm2
  • C 49 cm2
  • D 25 cm2

Question - 8

The ratio of areas of two similar triangles is 81 : 49. If the median of one triangle is 4.9 cm, what is the median of the other?

  • A 4.9 cm
  • B 6.3 cm
  • C 7 cm
  • D 9 cm

Question - 9

The perimeters of two similar triangles ABC and DEF are 24 cm and 32 cm respectively. If DE = 12 cm, find AB.

  • A 9cm
  • B 35 cm
  • C 18 cm
  • D 28 cm

Question - 10

BCand EFare the corresponding sides of two similar triangles ABC and DEF. lf BC = 9.1 cm, EF= 6.5 cm and the perimeter of \(\triangle\)DEF is 35 cm, find the perimeter of \(\triangle\) ABC.

  • A 15cm
  • B 49 cm
  • C 45 cm
  • D 35 cm
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