Question

In given fig, S and T are points on side PQ and PR respectively of triangle PQR, such that PT = 2cm and TR =4cm and ST parallel QR, find area of triangle PST/ area of triangle PQT​

Answer 1

$\huge\tt\fcolorbox{cyan}{plum}{ answer♡࿐}$

Given :

ST || QR, TR = 4 cm and PT = 2 cm.

So,

PR = 6 cm. In ΔPST and ΔPQR, ∠PST = ∠PQR ( corroesponding Angles)

∠PTS = ∠PRQ (Corresponding Angles )

∠P = ∠P ( common Angles )

We know that,

AAA similarity criterion states that in two triangles,

if corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

∴ ΔPST ~ ΔPQR We know that the ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

∴ ar (ΔPST): ar (ΔPQR) = 1: 9

${\huge{\underline{\small{\mathbb{\pink{So, \ (ΔPAT): \ ar \ (ΔPQR = 1:9}}}}}}$

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$\sf\red{Thank\:you!}$