SSC CGL 2024 Tier-I · 24 September 2024, Shift 2 · Quantitative Aptitude · Question 12 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

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?

Answer

Why

Correct — D. The stem is printed as an image: in ΔDEF, DE = 12 cm, EF = 15 cm and ∠DEF = 90°, ΔDEF is congruent to ΔXYZ, YZ = 15 cm, and XZ is wanted.

The congruence is written DEF ↔ XYZ, so D pairs with X, E with Y, F with Z. XZ is therefore the partner of DF, and the given YZ = 15 cm confirms EF = 15 cm.

∠DEF is the angle at E, so DE and EF are the legs:
DF² = 12² + 15² = 144 + 225 = 369
DF = √369 = √(9 × 41) = 3√41 cm

XZ = DF = 3√41 cm, the value printed on option (d).

Why the others are wrong

(a)
Option (a) shows 5√41, which squares to 25 × 41 = 1025. The two legs give 369, not 1025.
(b)
Option (b) shows 4√41, squaring to 16 × 41 = 656. Same slip in the other direction: 369 needs a coefficient of 3 outside the root.
(c)
Option (c) shows 2√41, squaring to 4 × 41 = 164. That is what 369 would give if the square factor pulled out were 4, but the square factor of 369 is 9.

Concept

A congruence statement is read letter by letter. ΔDEF ≅ ΔXYZ pairs D with X, E with Y and F with Z, so DE = XY, EF = YZ and DF = XZ — sides in the same position, not sides that look alike.

The right angle sits at the middle letter of ∠DEF, that is at E. So the two given sides are the legs, and the side opposite, DF, is the hypotenuse found by Pythagoras.

Every option is a multiple of √41, so the item finally turns on simplifying √369: 369 = 9 × 41 and √9 = 3.

The YZ = 15 cm in the stem is a consistency check rather than fresh information — through the correspondence it just repeats EF. The length can be found from ΔDEF alone.

Key facts

In ΔDEF ≅ ΔXYZ the correspondence D↔X, E↔Y, F↔Z makes DF the partner of XZ.
∠DEF names the angle at E, the middle letter of the three.
12² + 15² = 369, and 369 = 9 × 41, so √369 = 3√41.
CPCT: corresponding parts of congruent triangles are equal, taken in the stated letter order.

Study next

Reading a congruence statement for which sides correspondSimplifying surds by pulling out the largest square factorThe congruence criteria SSS, SAS, ASA, AAS and RHS

Common traps

Reading ∠DEF as the angle at D and treating EF as the hypotenuse.
Pairing XZ with EF instead of DF, which the letter order rules out.
Leaving the answer as √369 when the options are written in a√b form.

The lettering carries the work. 24 Sep 2024, 16:00, Quant Q.2 turns on the same reading: it asks which triangle the medial triangle DEF is NOT congruent to, when D, E and F are the mid-points of AB, BC and AC.

Related PYQs

No directly related past PYQ was found.