SSC CGL 2024 Tier-I · 9 September 2024, Shift 3 · Quantitative Aptitude · Question 21 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 6 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.

Two triangles EFG and HIJ are congruent. If the area of ΔEFG is 124 cm 2 , then the area of ΔHIJ will be:

(a)31 cm
(b)248 cm
(c)124 cm
(d)62 cm

Answer

Why

Correct — C. Congruent means the two triangles are the same figure in a different position, so every corresponding side, every angle and the area itself carry across unchanged.

ΔEFG ≅ ΔHIJ
area(ΔEFG) = 124
area(ΔHIJ) = area(ΔEFG) = 124 → option (c)

No ratio work is called for. Congruence is similarity with a scale factor of 1, so the area ratio is 1² = 1.

Why the others are wrong

(a)
31 cm — 31 is a quarter of 124 — the area of a similar triangle at half the scale. Congruence pins the scale factor at 1, so no shrinking applies.
(b)
248 cm — 248 doubles the area. Even in a similar triangle, doubling the sides multiplies area by four rather than two, and congruence changes the sides not at all.
(d)
62 cm — 62 halves the area. Congruent triangles are identical copies, and the stem introduces no second triangle of a different size.

Concept

Two triangles are congruent when one can be laid exactly over the other — all three sides and all three angles equal. The tests are SSS, SAS, ASA, AAS and RHS.

Congruent figures share every measurement, so perimeter and area transfer directly with no calculation.

Similar triangles are the weaker relation: equal angles, sides in a fixed ratio k, and areas in the ratio k². Only k = 1 makes similar triangles congruent.

The whole question is that distinction — it tests whether you reach for a ratio the stem never gave you.

The stem prints the given area as 'cm 2', the paper's rendering of cm², while the options are printed as plain 'cm'. That is the paper's own typography, not a change of unit: the quantity asked for is an area, and congruence hands it over unchanged at 124 cm².

Key facts

Congruent triangles have equal corresponding sides, equal corresponding angles and equal areas.
Similar triangles with side ratio k have areas in the ratio k².
Congruence is the case k = 1, so the area ratio is 1.
AAA establishes similarity only — equal angles fix shape but not size.

Study next

The five congruence criteria and the cases where RHS is the only one that worksArea ratio of similar triangles as the square of the side ratioWhy AAA gives similarity but never congruence

Common traps

Treating congruence as similarity and hunting for a scale factor the stem never supplies.
Doubling or halving because EFG and HIJ look like differently sized triangles.
Rejecting every option over the missing square in the printed unit.

SSC uses congruence as a one-line recall item where an area or a perimeter simply carries across. The harder version of the same stem swaps in the word 'similar' and supplies a side ratio, which turns it into a k² calculation.

Related PYQs

No directly related past PYQ was found.