Skip to content
doubtly

In the given figure, AR ⊥ BC, AR ⊥ PQ, then complete the activity for finding \(\dfrac{A(\Delta ABC)}{A(\Delta APQ)}\).[Figure: Δ ABC with A at the top; B, P, R, Q, C lie on the base line in that order; seg AR is drawn from A to the base with a right…

Q.2 (A)(1) In the given figure, AR ⊥ BC, AR ⊥ PQ, then complete the activity for finding \(\dfrac{A(\Delta ABC)}{A(\Delta APQ)}\).

[Figure: Δ ABC with A at the top; B, P, R, Q, C lie on the base line in that order; seg AR is drawn from A to the base with a right-angle mark at R on BC.]

Activity :

\(\dfrac{A(\Delta ABC)}{A(\Delta APQ)} = \dfrac{____ \times AR}{PQ \times ____}\)

\(\therefore \dfrac{A(\Delta ABC)}{A(\Delta APQ)} = \dfrac{____}{____}\)

1 answer

Best answer

Answer: the blanks are BC, AR and \(\dfrac{BC}{PQ}\).

Both triangles have the same height AR (AR ⊥ BC and AR ⊥ PQ), so the ratio of their areas equals the ratio of their bases:

\(\dfrac{A(\Delta ABC)}{A(\Delta APQ)} = \dfrac{\frac12 \times BC \times AR}{\frac12 \times PQ \times AR} = \dfrac{BC \times AR}{PQ \times AR} = \dfrac{BC}{PQ}\).

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report
Was this answer helpful?

Your answer

Log in or create a free account to answer this question.