SSC CGL 2025 Tier-I · 22 September 2025, Shift 1 · Quantitative Aptitude · Question 9 of 98

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 area of a regular triangle increases by 44%. By what percentage did the side length increase?

(a)20%
(b)44%
(c)54%
(d)10%

Answer

Why

Correct — A. A regular (equilateral) triangle has area (√3⁄4)a², so its area scales with the square of the side.

New area factor: 1 + 44⁄100 = 1.44
Side factor: √1.44 = 1.2
Increase in side: 1.2 − 1 = 0.2 = 20% → option (a)

Check: 1.2² = 1.44, an area 44% larger.

Why the others are wrong

(b)
44% — 44% treats the side as growing in step with the area. A 44% longer side would multiply the area by 1.44² ≈ 2.07, a 107% rise.
(c)
54% — A 54% longer side multiplies the area by 1.54² ≈ 2.37, more than double. The area here rose by 44%, not 137%.
(d)
10% — A 10% longer side gives 1.1² = 1.21, a 21% larger area, as in Quant Q.4 of 22 Sep 2025, 09:00. The area here rose by 44%.

Concept

For similar figures, area is proportional to the square of a length. An equilateral triangle's area is (√3⁄4)a², and the √3⁄4 cancels when two areas are compared.

To turn an area change into a side change, take the square root of the area factor, then subtract 1.

Here √1.44 = 1.2, so a 44% larger area needs a 20% longer side.

A regular triangle has all three sides equal, the same figure as an equilateral triangle. Any two equilateral triangles are similar, so the square law applies directly.

Key facts

Area of an equilateral triangle with side a = (√3⁄4)a².
Area factor = (side factor)², so side factor = √(area factor).
An area 44% larger means a side factor of √1.44 = 1.2, a 20% longer side.

Study next

Percentage change in perimeter from a given change in areaHeight of an equilateral triangle, (√3⁄2)aSimilar triangles: the ratio of areas equals the square of the ratio of sides

Common traps

Carrying the 44% straight across to the side, as if area grew in step with length.
Halving 44% to 22%: the square root of a growth factor is not half of the percentage.

Here an area change is given and the side change is asked, the square law run backwards. The forward direction is asked at 22 Sep 2025, 09:00, Quant Q.4 (a sphere's radius up 10%) and 12 Sep 2025, 16:00, Quant Q.22 (a disc's radius down 10%).

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.