SSC CGL 2024 Tier-I · 17 September 2024, Shift 3 · Quantitative Aptitude · Question 24 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.

If a triangle has a perimeter of 52 units, then all its sides have length ________ units.

(a)<24
(b)<20
(c)<26
(d)<18

Answer

Why

Correct — C. The triangle inequality says every side is shorter than the sum of the other two.

Let one side be s. The other two together come to 52 − s.
s < 52 − s
2s < 52
s < 26

The argument applies to whichever side you call s, so all three are under 26 units → option (c).
The bound is tight: sides of 25.9, 25.9 and 0.2 give a perimeter of 52 and a genuine triangle.

Why the others are wrong

(a)
<24 — <24 is not forced. Sides of 25, 25 and 2 total 52 and satisfy every triangle inequality, yet two of them exceed 24 — one real counterexample is enough to sink the claim.
(b)
<20 — <20 breaks on that same triangle of 25, 25 and 2. It holds for many triangles of perimeter 52, but the question asks what must be true of all of them.
(d)
<18 — <18 is the most restrictive of the four. An equilateral triangle of perimeter 52 has sides of 52⁄3 ≈ 17.33 and does satisfy it, but 25, 25 and 2 is equally a triangle of perimeter 52 and does not.

Concept

For three lengths to close into a triangle, each must be less than the sum of the other two — the triangle inequality. Fix the perimeter at 52 and the other two always sum to 52 minus the side itself.

That turns the condition into s < 52 − s, so s < 26. Since 26 is half of 52, the result generalises: no side of a triangle can reach half its perimeter.

The bound cannot be tightened. A side can come as close to 26 as you like, so any stricter claim — under 24, under 20, under 18 — is false for some triangle of perimeter 52.

The question asks what holds for every triangle of this perimeter, not what holds for a typical one. An equilateral triangle here has sides of about 17.33, which satisfies all four options at once — testing that case alone leaves you with no way to choose between them.

Key facts

Each side of a triangle is less than the sum of the other two.
With perimeter p, every side must be less than p⁄2.
For p = 52 that bound is 26 units.
Sides of 25, 25 and 2 form a valid triangle of perimeter 52, which defeats the bounds of 24, 20 and 18.

Study next

Range of the third side when the other two sides are givenCounting the integer values a side may take under the triangle inequalityWhy two sides summing to more than the third is enough to build the triangle

Common traps

Picking the tightest-looking bound rather than the one true of every such triangle
Testing only the equilateral case, where all four options happen to hold
Reading the blank as the largest side a triangle can have rather than a strict upper bound

SSC asks the triangle inequality as a bound, as here, and as a count. Quant Q.4 of this paper gives sides of 6 units and 12 units and asks how many integer values the third side can take — the same inequality read from the other end.

Related PYQs

No directly related past PYQ was found.