SSC CGL 2025 Tier-I · 23 September 2025, Shift 3 · Quantitative Aptitude · Question 9 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

The ratio of areas of two regular polygons with same number of sides is 4:9. What is the ratio of their side lengths?

(a)2:3
(b)4:5
(c)1 : √2
(d)2 : √5

Answer

Why

Correct — A. Two regular polygons with the same number of sides are similar, so their areas are in the ratio of the squares of their sides.

Set up: (side₁ : side₂)² = 4 : 9
Take square roots: side₁ : side₂ = √4 : √9
= 2 : 3 → option (a)

Why the others are wrong

(b)
4:5 — 4 : 5 squared gives areas of 16 : 25, not 4 : 9.
(c)
1 : √2 — 1 : √2 squared gives areas of 1 : 2, not 4 : 9.
(d)
2 : √5 — 2 : √5 squares to areas of 4 : 5. Its first term is √4, but its second should be √9 = 3, not √5.

Concept

Regular polygons with the same number of sides have equal angles and sides in one fixed proportion, so any two of them are similar. For similar figures, every length scales by k and every area by k².

So going from an area ratio to a side ratio means taking the square root of each term. Going from sides to areas means squaring. Perimeters and diagonals scale like sides.

The stem's condition same number of sides matters: a regular triangle and a regular hexagon are not similar, and their area ratio says nothing direct about their sides.

Key facts

For similar figures, area ratio = (side ratio)².
Regular polygons with the same number of sides are always similar.
The perimeter ratio of similar figures equals their side ratio, 2 : 3 here.

Study next

Volume ratio of similar solids = (side ratio)³Similar triangles: ratios of altitudes, medians and areasArea of a regular hexagon, (3√3⁄2) a²

Common traps

Copying the area ratio's terms into the side ratio instead of taking their square roots.
Squaring instead of rooting, which gives 16 : 81, a ratio not among the choices.

Here the area ratio is given and the side ratio asked. The same step runs on similar triangles at 11 Sep 2024, 12:30, Quant Q.4 (areas 25 : 144, sides 5 : 12), and at 24 Sep 2025, 16:00, Quant Q.11 it runs the other way, from a hexagon perimeter ratio of 5 : 7 to an area of 147 cm².

Related PYQs

No directly related past PYQ was found.

Topic: Triangle, Quadrilaterals, Regular Polygons, Circle — all 97 SSC CGL questions on it, every solved shift.