SSC CGL 2025 Tier-I · 14 September 2025, Shift 3 · Quantitative Aptitude · Question 21 of 95

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.

In similar triangles, the ratio of corresponding altitudes is 2:5. What is the ratio of their areas?

(a)2:5
(b)4:25
(c)2:25
(d)5:2

Answer

Why

Correct — B.
Rule: in similar triangles every pair of corresponding lengths is in one ratio k, and areas are in k².

Altitude ratio: k = 2 : 5
Square both terms: 2² : 5²
Area ratio = 4 : 25 → option (b)

Why the others are wrong

(a)
2:5 — 2 : 5 is the length ratio itself. Altitudes, sides and perimeters share it, but an area multiplies two lengths, so the ratio must be squared.
(c)
2:25 — 2 : 25 squares only the second term. Both terms square together: 2² : 5² = 4 : 25.
(d)
5:2 — 5 : 2 reverses the order and leaves it unsquared. The areas follow the altitudes in the order 2 : 5, squared to 4 : 25.

Concept

Similar triangles are scaled copies: one scale factor k multiplies every length, so sides, altitudes, medians and perimeters all keep the ratio k.

A triangle's area is ½ × base × height, a product of two lengths, so it scales by k × k = k².

Here base and altitude each scale by 2⁄5, so the area scales by (2⁄5) × (2⁄5) = 4⁄25.

The stem gives altitudes rather than sides. That changes nothing: in similar triangles the ratio of corresponding altitudes equals the ratio of corresponding sides.

Key facts

In similar triangles, corresponding sides, altitudes, medians and perimeters are all in the same ratio.
The ratio of the areas of similar triangles is the square of that ratio.
Going back from areas to lengths takes a square root: areas 25 : 144 give sides 5 : 12.

Study next

Finding the side ratio from an area ratio by taking square rootsSplitting a known total area between two similar triangles in a given side ratioThe triangle cut off by a line parallel to one side (basic proportionality theorem)

Common traps

Stopping at 2 : 5 because the stem already prints a ratio.
Squaring a perimeter ratio too: perimeters stay in the length ratio, only areas square.

This stem gives the altitude ratio and asks for areas. The reverse, areas 25 : 144 to sides 5 : 12, is asked 11 Sep 2024, 12:30, Quant Q.4, and sides 3 : 5 to areas 9 : 25 at 12 Sep 2025, 12:30, Quant Q.22.

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.