Question 232 marksVery Short AnswerSection B

  1. (B) In the figure given above, △ABC∼△XYZ\triangle ABC \sim \triangle XYZ, then find the values of x and y. (△ABC\triangle ABC: AB=4 cm,BC=6 cm,AC=yAB = 4 \text{ cm}, BC = 6 \text{ cm}, AC = y; △XYZ\triangle XYZ: XY=x,YZ=7.2 cm,XZ=6 cmXY = x, YZ = 7.2 \text{ cm}, XZ = 6 \text{ cm})

Triangles
Corresponding sides of similar triangles

Official answer

x=4.8 cmx = 4.8 \text{ cm} and y=5 cmy = 5 \text{ cm}. Since △ABC∼△XYZ\triangle ABC \sim \triangle XYZ, corresponding sides give the scale factor BCYZ=67.2=56\frac{BC}{YZ} = \frac{6}{7.2} = \frac{5}{6}, so ABXY=56\frac{AB}{XY} = \frac{5}{6} gives x=4.8 cmx = 4.8 \text{ cm} and ACXZ=56\frac{AC}{XZ} = \frac{5}{6} gives y=5 cmy = 5 \text{ cm}.

Answer keywords:similar triangles corresponding sides△ABC ~ △XYZAB/XY = BC/YZ = AC/XZscale factor 5/6x = 4.8 cmy = 5 cmratio of sides

Marking scheme

  1. 1.½ mark: Writing the correct correspondence ABXY=BCYZ=ACXZ\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}.
  2. 2.½ mark: Finding the scale factor 67.2=56\frac{6}{7.2} = \frac{5}{6}.
  3. 3.½ mark: Correct value x=4.8 cmx = 4.8 \text{ cm}.
  4. 4.½ mark: Correct value y=5 cmy = 5 \text{ cm} (units required for full marks).

Hint

Write corresponding sides in letter order: ABXY=BCYZ=ACXZ\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}. First find the fully-known ratio 67.2=56\frac{6}{7.2} = \frac{5}{6} — that scale factor gives both x and y.

Quick oral answer

Because △ABC∼△XYZ\triangle ABC \sim \triangle XYZ, corresponding sides are proportional in letter order, so ABXY=BCYZ=ACXZ\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}; the known ratio BCYZ=67.2=56\frac{BC}{YZ} = \frac{6}{7.2} = \frac{5}{6} is the scale factor, giving x=4.8 cmx = 4.8 \text{ cm} and y=5 cmy = 5 \text{ cm}.

Common mistakes

  1. 1.Mismatching corresponding sides — e.g. pairing BC with XZ instead of YZ — because the letter order of the similarity statement was ignored.
  2. 2.Inverting a ratio, writing x4=56\frac{x}{4} = \frac{5}{6} instead of 4x=56\frac{4}{x} = \frac{5}{6}, which gives x=103x = \frac{10}{3} instead of 4.8.
  3. 3.Dropping units or leaving x as an ugly decimal without simplifying 67.2\frac{6}{7.2} to the exact fraction 56\frac{5}{6} first, causing rounding errors.

Analysis and explanation

This question uses the definition of similar triangles, where corresponding sides follow the letter-order of the similarity statement.


Concept

  • △ABC∼△XYZ⇒ABXY=BCYZ=ACXZ\triangle ABC \sim \triangle XYZ \Rightarrow \frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ} (A↔X,B↔Y,C↔ZA \leftrightarrow X, B \leftrightarrow Y, C \leftrightarrow Z).
  • Compute the scale factor first using the one ratio with both sides known: BCYZ=67.2=56\frac{BC}{YZ} = \frac{6}{7.2} = \frac{5}{6}.

Key points

  • Using k=56k = \frac{5}{6}: 4x=56⇒x=4.8 cm\frac{4}{x} = \frac{5}{6} \Rightarrow x = 4.8 \text{ cm}; y6=56⇒y=5 cm\frac{y}{6} = \frac{5}{6} \Rightarrow y = 5 \text{ cm}.
  • Verify all three ratios equal 56\frac{5}{6} for consistency.

Common mistakes

  • Mismatching corresponding sides (e.g. pairing AB with YZ) because they 'look' similar in size instead of following the letter order.
  • Inverting the ratio (writing x4=56\frac{x}{4} = \frac{5}{6}) or mishandling the decimal 7.2 — converting it to 5/6 early avoids errors.

Interesting facts

The scale factor of similar figures affects area by its SQUARE: here k=56k = \frac{5}{6}, so area(ABC)area(XYZ)=2536\frac{\text{area}(ABC)}{\text{area}(XYZ)} = \frac{25}{36} — a fact CBSE loves to combine with side-ratio questions.

Similarity is the mathematical basis of scale models, maps, and photographic enlargements: every point is scaled by the same factor while all angles are preserved.

Question details

Q23 of 53 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Basic)
Year
2026
Section
Section B
Marks
2
Type
Very Short Answer
Chapter
Triangles
Topic
Corresponding sides of similar triangles
Bloom's level
apply
Syllabus topic
Unit 4: Geometry — Triangles: Similar Triangles and Ratio of Corresponding Sides
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

How do I know which sides correspond in △ABC∼△XYZ\triangle ABC \sim \triangle XYZ?

Follow the letter order of the similarity statement: A↔X,B↔Y,C↔ZA \leftrightarrow X, B \leftrightarrow Y, C \leftrightarrow Z. So AB corresponds to XY, BC to YZ, and AC to XZ, giving ABXY=BCYZ=ACXZ\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}.

What is the scale factor in this problem?

Use the pair where both sides are known: BCYZ=67.2=56\frac{BC}{YZ} = \frac{6}{7.2} = \frac{5}{6}. This 56\frac{5}{6} is the constant scale factor that every corresponding pair of sides must satisfy.

How are x and y found from the scale factor?

Set each unknown pair equal to 56\frac{5}{6}: 4x=56 gives x=245=4.8 cm\frac{4}{x} = \frac{5}{6} \text{ gives } x = \frac{24}{5} = 4.8 \text{ cm}, and y6=56 gives y=5 cm\frac{y}{6} = \frac{5}{6} \text{ gives } y = 5 \text{ cm}.