SSC CGL 2025 Tier-I · 17 September 2025, Shift 1 · Quantitative Aptitude · Question 20 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.

Where this paper and its answers come from

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 triangle ABC is 16 cm². If a similar triangle DEF has sides that are twice the length of △ABC's sides, what is the area of △DEF?

(a)32 cm²
(b)48 cm²
(c)64 cm²
(d)80 cm²

Answer

Why

Correct — C.
Rule: areas of similar triangles are in the ratio of the squares of their sides.

Side ratio DEF : ABC = 2 : 1
Area ratio = 2² : 1² = 4 : 1
Area of DEF = 4 × 16 = 64 cm² → option (c)

Why the others are wrong

(a)
32 cm² — 32 cm² doubles the area along with the sides. Area is length × length, so doubling every side multiplies it by 2 × 2 = 4, not by 2.
(b)
48 cm² — 48 cm² is 3 × 16, a scale factor with no basis in the question. Doubling the sides multiplies the area by 2² = 4, giving 64 cm².
(d)
80 cm² — 80 cm² is 16 + 64, the two areas added together. The question asks for the area of DEF alone, which is 4 × 16 = 64 cm².

Concept

Similar triangles have the same shape: every side of one is the same multiple k of the matching side of the other.

Area is a length times a length, so it scales by k². Perimeters, heights and medians are single lengths, so they scale by k.

Here k = 2, so the area grows 4 times. Had the sides tripled, it would grow 9 times.

Neither triangle's base or height is needed. The side ratio alone fixes the area ratio, which is why 16 cm² and the factor 2 are enough.

Key facts

If similar figures have sides in the ratio a : b, their areas are in the ratio a² : b².
Perimeters, heights and medians of similar triangles are in the same ratio as their sides.
Doubling every side of a triangle multiplies its area by 4.

Study next

Finding the side ratio from an area ratio by taking square rootsVolumes of similar solids, which scale by the cube of the side ratioArea ratios of similar polygons other than triangles

Common traps

Scaling the area by the side ratio (× 2) instead of its square (× 4)
Squaring again when going the other way: an area ratio of 4 : 1 means sides in the ratio 2 : 1, not 16 : 1

11 Sep 2024, 12:30, Quant Q.4 runs the square law in reverse: areas 25 : 144 give sides 5 : 12. 19 Sep 2025, 09:00, Quant Q.19 triples the sides of a 5-12-13 triangle, so its 30 cm² area becomes 9 × 30 = 270 cm².

Related PYQs

No directly related past PYQ was found.

Topic: Congruence and similarity of triangles — all 25 SSC CGL questions on it, every solved shift.