SSC CGL 2024 Tier-I · 13 September 2024, Shift 3 · Quantitative Aptitude · Question 5 of 98

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.

The perimeters of two similar triangles ΔRST and ΔABC are 26 cm and 39 cm, respectively. If AB = 24 cm, then RS is ___.

(a)24 cm
(b)16 cm
(c)18 cm
(d)36 cm

Answer

Why

Correct — B. In similar triangles every length scales by the same factor, and a perimeter is a length — so the ratio of perimeters is the ratio of corresponding sides.

Perimeters 26 : 39 = 2 : 3 (both divide by 13)

The naming ΔRST ~ ΔABC pairs R with A and S with B, so RS corresponds to AB.

RS ⁄ AB = 2⁄3
RS = 24 × 2⁄3 = 16 cm → option (b)

Why the others are wrong

(a)
24 cm — 24 cm is AB itself. The triangles are similar, not congruent — a perimeter ratio of 2 : 3 means every side of ΔRST is shorter than its partner in ΔABC.
(c)
18 cm — 18 cm is 24 × 3⁄4. No 3 : 4 appears anywhere here; 26 : 39 reduces to 2 : 3, and 24 × 2⁄3 is 16.
(d)
36 cm — 36 cm uses the ratio upside down, 24 × 3⁄2. ΔRST has the smaller perimeter, 26 against 39, so its side must come out below 24, not above.

Concept

Similar triangles have equal corresponding angles and a single constant ratio k between corresponding sides.

That constant governs every linear measure — each side, the perimeter, every median, every altitude, the inradius. Areas do not follow k; they follow k².

So the first thing to settle in any similarity question is which kind of quantity you have been handed. A perimeter is linear, so use k directly. An area needs a square root before it becomes k.

The similarity statement, not a picture, tells you which side pairs with which. Written the other way round, ΔRST ~ ΔBAC, the same numbers would be solving for a different segment.

Key facts

In similar triangles the ratio of perimeters equals the ratio of corresponding sides.
The ratio of areas of similar triangles is the square of the side ratio.
26 : 39 reduces to 2 : 3, both terms sharing the factor 13.
The letter order in ΔRST ~ ΔABC fixes the pairing R–A, S–B, T–C.

Study next

Ratio of areas of similar triangles, which is the square of the side ratioBasic Proportionality Theorem and the similar triangles a parallel line createsThe similarity criteria AA, SSS and SAS, and which one a question hands you

Common traps

Inverting the scale factor and multiplying by 3⁄2 instead of 2⁄3.
Taking a square root, as an area ratio would demand, when the given ratio is of perimeters.
Pairing RS with BC because no diagram is supplied to correct you.

The squared form of the very same rule is set at 11 Sep 2024, 12:30, Quant Q.4, where an area ratio of 25 : 144 must be turned back into a side ratio.

Between them the two questions cover the whole rule: perimeters scale by k, areas by k².

Related PYQs

No directly related past PYQ was found.