Question

In triangle PQR ST||PQ and 2A(∆RST)=A(quadrilateral PQTS)then find RS:PR and show that PQ=√3×ST with method​

Answer 1

Given :-

• In triangle PQR ST || PQ .
• 2A( ∆ RST ) = A(quadrilateral PQTS)

To Find :-

• RS : PR ?
• show that PQ = √3×ST .

Solution :-

Given that,

→ 2 * Area(∆RST) = Area (quadrilateral PQTS)

So,

→ Area ∆RPQ = Area(∆RST) + Area (quadrilateral PQTS)

→ Area ∆RPQ = Area(∆RST) + 2 * Area(∆RST)

→ Area ∆RPQ = 3{Area(∆RST)}

→ Area(∆RST) / Area (∆RPQ) = 1/3

Also,

→ ST || PQ

Therefore,

→ (RS / PR)² = (ST/PQ)² = Area(∆RST) / Area (∆RPQ) { The ratio of the areas of two similar triangles is equal to the square of ratio of their corresponding sides. }

Hence,

→ (RS / PR)² = 1/3

→ RS / PR = (1/√3) (Ans.)

Also,

→ (ST/PQ)² = 1/3

→ (ST / PQ) = (1/√3)

→ PQ = √3•ST (Proved).

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