SSC CGL 2025 Tier-I · 12 September 2025, Shift 2 · Quantitative Aptitude · Question 22 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.

Two triangles are similar with sides in the ratio 3:5. What is the ratio of their areas?

(a)3:5
(b)5:3
(c)9:25
(d)25:9

Answer

Why

Correct — C. Area is ½ × base × height, and in similar triangles the base and the height both scale by the side ratio.

Side ratio = 3 : 5
Area ratio = 3² : 5² (two lengths multiplied)
= 9 : 25 → option (c)

Why the others are wrong

(a)
3:5 — 3 : 5 is the side ratio itself. It also holds for perimeters, altitudes and medians, but area multiplies two lengths, so it is squared.
(b)
5:3 — 5 : 3 reverses the order and still does not square. The areas follow the sides' order, first triangle to second.
(d)
25:9 — 25 : 9 squares correctly but flips the order. The first triangle has the shorter sides, so it has the smaller area: 9 : 25.

Concept

Similar triangles have equal angles, and every pair of corresponding lengths is in one ratio, k. Sides, perimeters, altitudes and medians all scale by k.

Area multiplies two lengths, so it scales by k². With k = 3⁄5, the areas are in 9 : 25.

To get sides from areas, run it backwards and take square roots.

The rule is not special to triangles. Areas of any two similar figures go as the square of the length ratio, and volumes of similar solids as the cube.

Key facts

Similar triangles with side ratio a : b have area ratio a² : b².
Perimeters, altitudes and medians of similar triangles are in the side ratio, not its square.
From an area ratio, take square roots for the side ratio: 25 : 144 gives 5 : 12.

Study next

Area ratio from an altitude or median ratioSplitting a total area in a squared ratioArea ratios when a line parallel to one side cuts a triangle

Common traps

Stopping at 3 : 5. That is the side ratio, and area needs it squared.
Squaring and then writing the larger area first. 25 : 9 answers the question asked second triangle to first.

The same 3 : 5 appears on 17 Sep 2025, 16:00, Quant Q.20 as a perimeter ratio: areas totalling 34 cm² split 9 : 25, so the larger is 25 cm².

The rule runs backwards on 11 Sep 2024, 12:30, Quant Q.4 (areas 25 : 144, sides 5 : 12) and through altitudes on 14 Sep 2025, 16:00, Quant Q.21 (altitudes 2 : 5, areas 4 : 25).

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.