In , let be the median to side . In , let be the median to side . It is given that ,…

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

In △ABC\triangle ABC, let ADAD be the median to side BCBC. In △PQR\triangle PQR, let PSPS be the median to side QRQR. It is given that AD=9 cmAD=9\,\text{cm}, PS=6 cmPS=6\,\text{cm}, and BC=15 cmBC=15\,\text{cm}. Further, ∠A=∠P\angle A=\angle P and ∠C=∠R\angle C=\angle R. (a) Prove that △ABC∼△PQR\triangle ABC\sim\triangle PQR. (b) Using part (a), calculate the length of QRQR. (c) If AB=13 cmAB=13\,\text{cm}, determine PQPQ. (d) Find the ratio [△ABC]:[△PQR][\triangle ABC]:[\triangle PQR].

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