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.

1 Verified Answer | Published on 05th 09, 2020

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

1 Verified Answer | Published on 05th 09, 2020

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) $\dfrac { { AB }^{ 2 } }{ { AC }^{ 2 } } = \dfrac { BD }{ DC }$

1 Verified Answer | Published on 05th 09, 2020

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. $5$

1 Verified Answer | Published on 05th 09, 2020

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. $0$

1 Verified Answer | Published on 05th 09, 2020

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. $\frac{1 + \sqrt 5}{2}$

1 Verified Answer | Published on 05th 09, 2020

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 $EF$.

1 Verified Answer | Published on 05th 09, 2020

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. $24"$

1 Verified Answer | Published on 05th 09, 2020

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

1 Verified Answer | Published on 05th 09, 2020

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.