SSC CGL 2024 Tier-I · 9 September 2024, Shift 1 · Quantitative Aptitude · Question 14 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.

If the sum of two sides of an equilateral triangle is 16 cm, then find the third side.

(a)Cannot be found
(b)16 cm
(c)4 cm
(d)8 cm

Answer

Why

Correct — D. In an equilateral triangle all three sides are equal, so call each side a.

Two sides sum to 16: a + a = 2a = 16
Divide by 2: a = 8 cm

The third side equals the other two, so it is 8 cm → option (d).
Sides 8, 8, 8 give a perimeter of 24 cm.

Why the others are wrong

(a)
Cannot be found — Cannot be found ignores what equilateral already tells you: one length fixes all three. No angle, area or second equation is needed.
(b)
16 cm — 16 cm is the sum of two sides, not one of them. A triangle with sides 16, 8 and 8 would be isosceles, and 8 + 8 = 16 means it collapses into a straight line.
(c)
4 cm — 4 cm comes from dividing 16 by 4 instead of by 2. Only two sides were added, so the divisor is 2.

Concept

This is a definition check, not a calculation. Equilateral means three equal sides, and therefore three 60° angles.

So the phrase 'sum of two sides' is just 2a in disguise, and one division finishes the question.

The check worth doing is the triangle inequality: 8 + 8 = 16 > 8, so a triangle with these sides genuinely exists.

Option (a) exists to catch candidates who expect every geometry item to need more data. Here the word equilateral is the missing data.

Key facts

An equilateral triangle has three equal sides and three 60° angles.
If two of its sides sum to 16 cm, each side is 8 cm and the perimeter is 24 cm.
Area of an equilateral triangle of side a is (√3⁄4)a², so this one measures 16√3 cm².

Study next

Height (√3⁄2)a and area (√3⁄4)a² of an equilateral triangleIsosceles and scalene triangles, where two sides never determine the thirdThe triangle inequality as the test of whether three lengths can close

Common traps

Reading 16 cm as one side instead of as the sum of two
Choosing 'Cannot be found' because no angle or area is stated
Dividing 16 by 3, as though 16 were the perimeter

This is the free mark of the set — a definition dressed as a problem. Same shift, Quant Q.5 does the same job for triangles by asking which single statement is enough to prove congruence.

Related PYQs

No directly related past PYQ was found.