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Triangles Maths - Triangles

Maharashtra Board - STD 10 - Maths (MSBSHSE - Semi English Medium). 254 questions in this chapter.

Question types

Triangles question types

254 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

254
Questions
5
Question groups
5
Question types
Sample Questions

Triangles questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
$\triangle\text{ABC}$ is a right triangle right$-$angled at $A$ and $\text{AD}\perp\text{BC}.$ Then, $\frac{\text{BD}}{\text{DC}}=$
  • ✓
    $\Big(\frac{\text{AB}}{\text{AC}}\Big)^2$
  • B
    $\frac{\text{AB}}{\text{AC}}$
  • C
    $\Big(\frac{\text{AB}}{\text{AD}}\Big)^2$
  • D
    $\frac{\text{AB}}{\text{AD}}$

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark
If $\triangle\text{ABC}\sim\triangle\text{DEF}$ such that $DE = 3\ cm, EF = 2\ cm, DF = 2.5\ cm, BC = 4\ cm,$ then perimeter of $\triangle\text{ABC}$ is:
  • A
    $18\ cm.$
  • B
    $20\ cm.$
  • C
    $12\ cm.$
  • ✓
    $15\ cm.$

Answer: D.

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Q 3M.C.Q (1 Marks)1 Mark
$\triangle\text{ABC}$ is such that $AB = 3\ cm, BC = 2\ cm$ and $CA = 2.5\ cm.$ If $\triangle\text{DEF}\sim\triangle\text{ABC}$ and $EF = 4\ cm,$ then perimeter of $\triangle\text{DEF}$ is:
  • A
    $7.5\ cm.$
  • ✓
    $15\ cm.$
  • C
    $22.5\ cm.$
  • D
    $30\ cm.$

Answer: B.

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Q 4M.C.Q (1 Marks)1 Mark
If $D, E, F$ are the mid-points of sides $BC, CA$ and $AB$ respectively of $\triangle\text{ABC},$ then the ratio of the areas of triangles $DEF$ and $ABC$ is:
  • ✓
    $1 : 4$
  • B
    $1 : 2$
  • C
    $2 : 3$
  • D
    $4 : 5$

Answer: A.

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Q 5M.C.Q (1 Marks)1 Mark
In a $\triangle\text{ABC},$ point $D$ is on side $AB$ and point $E$ is on side $AC,$ such that $\text{BCED}$ is a trapezium. If $\text{DE : BC} = 3 : 5,$ then $\text{Area}(\triangle\text{ADE}):\text{Area}(\Box\text{BCED})=$
  • A
    $3 : 4.$
  • ✓
    $9 : 16.$
  • C
    $3 : 5.$
  • D
    $9 : 25.$

Answer: B.

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Q 82 Marks Questions2 Marks
Triangle ABC and DEF are similar.
If area $\big(\triangle\text{ABC}\big) =16\text{cm}^2,$ area $\big(\triangle\text{DEF}\big) =25\text{cm}^2 $ and BC = 2.3cm, find EF.
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Q 92 Marks Questions2 Marks
In a $\triangle\text{ABC,D}\ \text{and E}$ are points on the sides AB and AC respectively such that DE || BC.
If AD = 4cm, DB = 4.5cm and AE = 8cm, find AC.
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Q 123 Marks Question3 Marks
In fig. $\triangle\text{ABC}$ is a triangle such that $\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{DC}},\angle\text{B}=70^\circ,\angle\text{C}=50^\circ.$ Find the $\angle\text{BAD}.$
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Q 143 Marks Question3 Marks
In $\triangle\text{ABC and }\triangle\text{DEF},$ it is being given that: AB = 5cm, BC = 4cm and CA = 4.2cm; DE = 10cm, EF = 8cm and FD = 8.4cm. If $\text{AL}\perp\text{BC}$ and $\text{DM} \perp \text{EF,}$ find AL : DM.
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Q 164 Marks Questions4 Marks
In $\triangle\text{ABC},$ D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of $\triangle\text{ADE}$ and $\triangle\text{ABC.}$
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Q 174 Marks Questions4 Marks
ABCD is a rectangle. Points M and N are on BD such that $\text{AM}\perp\text{BD}$ and $\text{CN}\perp\text{BD}.$ Prove that $BM^2 + BN^2= DM^2+ DN^2$​​​​​​​.
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Q 194 Marks Questions4 Marks
$A$ point $D$ is on the side $BC$ of an equilateral triangle $ABC$ such that $\text{DC}=\frac{1}{4}\text{BC}.$ Prove that $AD^2= 13\ CD^2$​​​​​​​
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Q 204 Marks Questions4 Marks
A guy wire attached to a vertical pole of height $18\ m$ is $24\ m$ long has a stake attached to the other end. How far from the base of pole should the stake be driven so that the wire will be taut?
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