In given figure, ST βˆ₯ RQ, PS = 3 cm and SR = 4 cm. Find the ratio of the area of βˆ†PST to the area of βˆ†PRQ.

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Question 5 In given figure, ST βˆ₯ RQ, PS = 3 cm and SR = 4 cm. Find the ratio of the area of βˆ†PST to the area of βˆ†PRQ. Given: Ξ” ABC ST II RQ PS = 3 cm, SR = 4cm To find : (π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑆𝑇)/(π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑅𝑄) Proof: In Ξ” PRQ & Ξ” PST, ∠ QPR = ∠ TPS ∠ PRQ = ∠ PST Ξ” PRQ ~ Ξ” PST Now, we know that in similar triangles, Ratio of area of triangle is equal to ratio of square of corresponding sides (π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑆𝑇)/(π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑅𝑄)=(𝑃𝑆/𝑃𝑅)^2 (π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑆𝑇)/(π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑅𝑄)=(𝑃𝑆/(𝑃𝑆 + 𝑆𝑅))^2 (π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑆𝑇)/(π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑅𝑄)=(3/(3 + 4))^2 (π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑆𝑇)/(π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑅𝑄)=(3/7)^2 (π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑆𝑇)/(π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑅𝑄)=9/49 ∴ Required Ratio = 9 : 49 (Putting PS = 3 cm, SR = 4 cm)

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