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SSC CHSL 2024 PYQ — Question 66

SSC CHSL - 01 July 2024 - Shift 4 • Quantitative Aptitude • Q66

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Diagonals of a trapezium ABCD with AB∥DC, intersect each other at the point ‘O’. If AB = 2.5CD, find the ratio of the area of triangle AOB to the area of triangle COD

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 25:4.

As seen in the figure

In ΔAOB and ΔCOD,

∠AOB = ∠COD (vertically opposite angles)

∠CDO = ∠ABO (alternate interior angles)

Hence, ΔAOB ~ ΔCOD (AA similarity criterion)

arΔAOBarΔCOD\frac{arΔAOB}{arΔCOD} = AB2 / CD2  = (2.5CD)2 / CD2 

Solving we get 

arΔAOBarΔCOD\frac{arΔAOB}{arΔCOD} = 254\frac{25}{4}

Hence, the ratio of the area of triangle AOB to the area of triangle COD is 25 : 4.