SSC CGL 2025 Tier-I · 17 September 2025, Shift 2 · Quantitative Aptitude · Question 19 of 99

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.

In a trapezoid ABCD with AB parallel to CD, the diagonals AC and BD intersect at E. What is the ratio of the area of △ABE to the area of △CDE?

(a)The ratio of AB to CD squared.
(b)The ratio of AB to CD.
(c)The ratio of the perimeter of △ABE to the perimeter of △CDE.
(d)The ratio of the area of △ABC to the area of △BCD.

Answer

Why

Correct — A. AB ∥ CD makes △ABE and △CDE similar.

∠EAB = ∠ECD (alternate angles, transversal AC)
∠EBA = ∠EDC (alternate angles, transversal BD)
∠AEB = ∠CED (vertically opposite)

So △ABE ~ △CDE, with side AB matching side CD
Similar triangles: area ratio = (side ratio)²
Area △ABE : area △CDE = (AB : CD)² → option (a)

Why the others are wrong

(b)
The ratio of AB to CD. — AB : CD is the side ratio, and also the ratio of the two triangles' heights from E. Area multiplies base by height, so the area ratio is that ratio squared.
(c)
The ratio of the perimeter of △ABE to the perimeter of △CDE. — Perimeters of similar triangles scale like their sides, so this ratio equals AB : CD, not its square. A perimeter is a length; an area is length × length.
(d)
The ratio of the area of △ABC to the area of △BCD. — △ABC and △BCD have the same height, the gap h between the parallel sides. Their areas are ½ × AB × h and ½ × CD × h, so the ratio is AB : CD, not squared.

Concept

Similar triangles: if each side of one triangle is k times the matching side of another, its perimeter is k times as long and its area is k² times as large.

In a trapezium the diagonals cut each other in the ratio of the parallel sides: AE : EC = BE : ED = AB : CD. The triangles standing on the two parallel sides are similar, so their areas go as (AB : CD)².

Read option (a) as the ratio AB : CD, squared. With AB = 12 and CD = 4, the sides are 3 : 1 and the areas 9 : 1.

Options (b), (c) and (d) all come to AB : CD. They would agree with (a) only if AB = CD, which would make the figure a parallelogram, not a trapezoid.

Key facts

Similar triangles with side ratio k have perimeters in the ratio k and areas in the ratio k².
In trapezium ABCD with AB ∥ CD, the diagonals divide each other in the ratio AB : CD.
Triangles on the same base and between the same parallels have equal areas.

Study next

Areas of all four triangles cut off by a trapezium's diagonalsBasic proportionality theorem: a line parallel to one side of a triangle divides the other two sides in the same ratioArea of a triangle against the trapezium cut off by a line parallel to its base

Common traps

Stopping at the side ratio AB : CD and not squaring it for the areas.
Picking option (d) because it also compares areas: triangles with the same height compare as their bases, not as squares.

Squaring a side ratio to compare areas also decides 15 Sep 2025, 09:00, Quant Q.20: △ADE : trapezium DECB = 4 : 21 makes △ADE : △ABC = 4 : 25, so AD : AB = 2 : 5 and AD : DB = 2 : 3.

Related PYQs

No directly related past PYQ was found.

Topic: Ratio & Proportion — all 96 SSC CGL questions on it, every solved shift.