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Triangles
CBSE 2026 Board Exam Set 3 (Code 30/1/3)
CBSE_BOARD_PYQ_2026_30_1_3
Grade 10
Question:
[Section B]
In $\Delta ABC$, $DE \parallel BC$ with $D$ on $AB$ and $E$ on $AC$. If $AD = x$, $DB = x - 2$, $AE = x + 2$, and $EC = x - 1$, find the value of $x$.
OR
If $\Delta ABC \sim \Delta XYZ$ such that $AB = 4$ cm, $XY = x$ cm, $BC = 6$ cm, $YZ = 7.2$ cm, and $XZ = 6$ cm, find the values of $x$ and $y$ (where $AC = y$).
In $\Delta ABC$, $DE \parallel BC$ with $D$ on $AB$ and $E$ on $AC$. If $AD = x$, $DB = x - 2$, $AE = x + 2$, and $EC = x - 1$, find the value of $x$.
OR
If $\Delta ABC \sim \Delta XYZ$ such that $AB = 4$ cm, $XY = x$ cm, $BC = 6$ cm, $YZ = 7.2$ cm, and $XZ = 6$ cm, find the values of $x$ and $y$ (where $AC = y$).
Step-by-Step Solution
Key Concept: BPT theorem OR Ratio of corresponding sides of similar triangles.
Main: By BPT, $\dfrac{x}{x-2} = \dfrac{x+2}{x-1} \Rightarrow x(x-1) = (x-2)(x+2) \Rightarrow x^2 - x = x^2 - 4 \Rightarrow x = 4$. [2.0 Marks]
OR: $\dfrac{AB}{XY} = \dfrac{BC}{YZ} = \dfrac{AC}{XZ} \Rightarrow \dfrac{4}{x} = \dfrac{6}{7.2} = \dfrac{y}{6}$. Solving gives $x = 4.8$ cm, $y = 5$ cm. [2.0 Marks]
OR: $\dfrac{AB}{XY} = \dfrac{BC}{YZ} = \dfrac{AC}{XZ} \Rightarrow \dfrac{4}{x} = \dfrac{6}{7.2} = \dfrac{y}{6}$. Solving gives $x = 4.8$ cm, $y = 5$ cm. [2.0 Marks]
Correct Answer: x = 4 OR x = 4.8 cm, y = 5 cm
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