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SSC CGL 2024 PYQ — Question 74

SSC CGL - 24 Sep 2024 - Shift 2 • Quantitative Aptitude • Q74

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In ΔDEF , DE = 12 cm, EF = 15 cm, and ∠DEF = 90°. ΔDEF is congruent to ΔXYZ. If YZ = 15 cm, then what is the length of XZ?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 341{\sqrt{41}} cm

DE = 12 cm, EF = 15 cm, ∠DEF = 90°, and YZ = 15 cm

ΔDEF is congruent to ΔXYZ. So, their corresponding sides are equal.

So, EF = YZ, DE = XY, DF =  XZ 

In ΔDEF, DF = √(DE2 + EF2)

= √(122 + 152)

= √(144 + 225)

= √369

= 3√41 cm

XZ = DF = 3√41 cm

Therefore, the length of XZ is 3√41 cm.