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Chapter: Similarity· Mathematics Part 2 (Geometry)

Asked in: March 2025 and March 2026 board papersIn the following figure, seg XY || seg AC. If 2AX = 3BX and XY = 9, complete the activity to find the value of AC.[Figure: \(\Delta ABC\) with X on side AB and Y on side BC, seg XY parallel to side AC.]…

Asked in: March 2025 and March 2026 board papers

In the following figure, seg XY || seg AC. If 2AX = 3BX and XY = 9, complete the activity to find the value of AC.

[Figure: \(\Delta ABC\) with X on side AB and Y on side BC, seg XY parallel to side AC.]

Activity: 2AX = 3BX (given) \(\therefore \dfrac{AX}{BX} = \dfrac{3}{\text{____}}\); \(\dfrac{AX + BX}{BX} = \dfrac{3 + 2}{2}\) (by componendo); \(\dfrac{\text{____}}{BX} = \dfrac{5}{2}\) ...... (I). Now \(\Delta BCA \sim \Delta BYX\) (____ test of similarity) \(\therefore \dfrac{BA}{BX} = \dfrac{AC}{XY}\) (corresponding sides of similar triangles) \(\therefore \dfrac{\text{____}}{\text{____}} = \dfrac{AC}{9}\) [from (I)] \(\therefore AC = \) ____

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Answer: AC = 22.5

2AX = 3BX \(\therefore \dfrac{AX}{BX} = \dfrac{3}{\boxed{2}}\)

\(\dfrac{AX + BX}{BX} = \dfrac{3 + 2}{2}\) ...... (by componendo)

\(\dfrac{\boxed{AB}}{BX} = \dfrac{5}{2}\) ...... (I)

In \(\Delta BCA\) and \(\Delta BYX\): \(\angle B\) is common and \(\angle BAC \cong \angle BXY\) (corresponding angles, XY || AC). So \(\Delta BCA \sim \Delta BYX\) ...... (AA test of similarity)

\(\therefore \dfrac{BA}{BX} = \dfrac{AC}{XY}\) \(\therefore \dfrac{\boxed{5}}{\boxed{2}} = \dfrac{AC}{9}\)

\(\therefore AC = \dfrac{5 \times 9}{2} = \boxed{22.5}\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report
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