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Triangles: CBSE Class 10 Mathematics practice questions

Practise 50 questions on Triangles, free, with an explanation for each answer.

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Sample questions

A photographer enlarges (makes bigger) a 3535 mm film into a 4545 mm print. A line measures 1414 mm on the film. How long will it be on the print?

A 35 mm photograph enlarged to a 45 mm print
  1. 24 mm
  2. about 10.9 mm
  3. 31 mm
  4. 18 mm
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D. 18 mm

Every line segment is enlarged in the ratio 35:4535:45, so the scale factor is 4535=97\dfrac{45}{35}=\dfrac{9}{7} and the line becomes 14×97=1814\times\dfrac{9}{7}=18 mm. Adding the 1010 mm difference gives 2424 mm, which is not a ratio. Using 3545\dfrac{35}{45} would shrink it (about 10.910.9 mm). Subtracting from 4545 (3131 mm) has no meaning.

A square of side 44 cm and a rectangle 66 cm by 44 cm both have all angles equal to 90∘90^\circ. Why are they not similar?

A square of side 4 cm and a rectangle 6 cm by 4 cm, all angles 90 degrees
  1. Their corresponding angles are not equal
  2. A square has fewer sides than a rectangle
  3. Their sides are not in the same ratio: 46≠44\dfrac{4}{6}\neq\dfrac{4}{4} for corresponding sides
  4. Figures of different sizes can never be similar
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C. Their sides are not in the same ratio: 46≠44\dfrac{4}{6}\neq\dfrac{4}{4} for corresponding sides

Two polygons are similar only if (i) corresponding angles are equal and (ii) corresponding sides are in the same ratio. Here (i) holds but the ratios are 46\dfrac{4}{6} and 44\dfrac{4}{4}, so (ii) fails. Both have four sides, and similar figures are allowed to differ in size.

In △ABC\triangle ABC, DE∥BCDE\parallel BC. Also, AD=xAD=x, DB=x−2DB=x-2, AE=x+2AE=x+2 and EC=x−1EC=x-1 (in cm). Find xx.

Triangle ABC with DE parallel to BC and sides marked x, x-2, x+2 and x-1
  1. x=25x=\dfrac{2}{5}
  2. x=−4x=-4
  3. x=4x=4
  4. x=23x=\dfrac{2}{3}
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C. x=4x=4

ADDB=AEEC⇒x(x−1)=(x−2)(x+2)⇒x2−x=x2−4⇒x=4\dfrac{AD}{DB}=\dfrac{AE}{EC}\Rightarrow x(x-1)=(x-2)(x+2)\Rightarrow x^2-x=x^2-4\Rightarrow x=4. Check: 42=63\dfrac{4}{2}=\dfrac{6}{3}. Traps: flipping one ratio, xx−2=x−1x+2\dfrac{x}{x-2}=\dfrac{x-1}{x+2}, gives 5x=25x=2, i.e. 25\frac25; writing (x+2)(x−2)=x2+4(x+2)(x-2)=x^2+4 gives −4-4; and pairing AD⋅DB=AE⋅ECAD\cdot DB=AE\cdot EC gives 23\frac23.

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