6

Triangles

10th Class - CBSE - Mathematics - 2263 Questions - 0 Concepts

Important Questions

Q1 Subjective Hard
If D is a point on the side AB of $$\triangle$$ ABC such  that AD : DB = 3:2 and E is a point on BC such that DE $$ \parallel$$ AC. Find the ratio of areas of $$\triangle$$ ABC and $$\triangle$$ BDE.

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Q2 Subjective Hard
In Figure AB$$=8$$ cm, BC$$=6$$cm, AC$$=3$$cm and the $$\angle $$ADC$$=90^{\circ}$$. Calculate CD.

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Q3 Subjective Hard
$$\triangle ABD $$ is a right triangle right-angled at A and  $$AC\bot BD.$$  Show that 
(i) $${ AB }^{ 2 } = BC.BD$$
(ii) $${ AC }^{ 2 } = BC.DC$$
(iii) $${ AD }^{ 2 } = BD \cdot CD$$
(iv) $$\dfrac { { AB }^{ 2 } }{ { AC }^{ 2 } } = \dfrac { BD  }{ DC }$$

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Q4 Single Correct Hard
What is the length 'x' of the line segment CD in the triangle drawn given?
  • A. $$4$$
  • B. $$6$$
  • C. $$8$$
  • D. $$5$$

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Q5 Single Correct Hard
Let $$ABCD$$ is a square with sides of unit length. Points $$E$$ and $$F$$ are on sides $$AB$$ and $$AD$$ respectively, so that $$AE = AF.$$ Let $$P$$ be a point inside square $$ABCD.$$

The value of $$(PA)^2 - (PB)^2 + (PC)^2 - (PD)^2$$ is equal to
  • A. $$3$$
  • B. $$2$$
  • C. $$1$$
  • D. $$0$$

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Q6 Single Correct Hard
$$\frac{a}{r}$$, a, ar are the sides of a triangle. If the triangle is a right angled triangle, then $$r^2$$ is given by
  • A. $$\frac{1 - \sqrt 5}{2}$$
  • B. $$\frac{-1 + \sqrt 5}{2}$$
  • C. $$\frac{- 1 + \sqrt 3}{2}$$
  • D. $$\frac{1 + \sqrt 5}{2}$$

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Q7 Subjective Hard
$$\triangle ABC \sim \triangle DEF$$ and the perimeters of $$\triangle ABC$$ and $$\triangle DEF$$ are $$30\ cm$$ and $$18\ cm$$ respectively. If $$BC = 9\ cm$$, find $$EF$$.

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Q8 Single Correct Hard
An isosceles triangle has a $$10$$ inch base and two $$13$$ inch sides. What other value can the base have and still yield a triangle with the same area?
  • A. $$18"$$
  • B. $$19"$$
  • C. $$27"$$
  • D. $$24"$$

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Q9 Single Correct Hard
In the figure, the value $$x$$ is equal to
  • A. $$4.2$$
  • B. $$0.8$$
  • C. $$0.4$$
  • D. $$3.2$$

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Q10 Subjective Hard
In a right triangle the lengths of the medians of the acute angles are $$9$$ cm and $$13$$ cm. Find the length of the hypotenuse of the triangle.

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Questions 122475
Subjects 10
Chapters 93
Enrolled Students 65
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