SSC CGL 2024 Tier-I · 11 September 2024, Shift 3 · Quantitative Aptitude · Question 8 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

In ∆ABC, two medians AD and BE intersect at G at right angles. If AD = 12 cm and BE = 9 cm, then the length of AB is equal to:

(a)12 cm
(b)14 cm
(c)10 cm
(d)16 cm

Answer

Why

Correct — C. The centroid G divides each median in the ratio 2 : 1 from the vertex.

AG = 2⁄3 × AD = 2⁄3 × 12 = 8 cm
BG = 2⁄3 × BE = 2⁄3 × 9 = 6 cm

AD and BE meet at right angles at G, so triangle AGB is right-angled at G:
AB² = AG² + BG² = 8² + 6² = 64 + 36 = 100
AB = 10 cm → option (c).

Why the others are wrong

(a)
12 cm — 12 cm is AD itself, the length of the median, not of the side. AB is the hypotenuse of the right triangle whose legs are the centroid segments 8 cm and 6 cm.
(b)
14 cm — 14 cm is 8 + 6, the two centroid segments added rather than combined. They meet at a right angle, so they compose as √(8² + 6²) = 10, not as a sum.
(d)
16 cm — 16 cm is longer than AG + BG. Nothing in the working produces it: the legs at G are 8 cm and 6 cm, and even their sum is only 14 cm.

Concept

The three medians of a triangle are concurrent at the centroid, which cuts each of them in the ratio 2 : 1 measured from the vertex. The longer piece is always the one touching the vertex.

So the median lengths 12 cm and 9 cm become segments of 8 cm and 6 cm at G. The perpendicularity given in the stem then turns a geometry question into a Pythagoras step.

Written generally, when the medians from A and B are perpendicular, AB² = 4⁄9 (AD² + BE²). Here 4⁄9 × (144 + 81) = 4⁄9 × 225 = 100.

The only figure-level fact you need is that G lies on both medians, so AG and BG are the legs of the right angle. No property of C or of the third median is used.

Key facts

The medians of a triangle meet at the centroid, which divides each in the ratio 2 : 1 from the vertex.
AG = 2⁄3 × 12 = 8 cm and BG = 2⁄3 × 9 = 6 cm.
With AD perpendicular to BE, AB² = AG² + BG² = 64 + 36 = 100, so AB = 10 cm.
The general form is AB² = 4⁄9 (AD² + BE²) when those two medians are perpendicular.

Study next

The 2 : 1 centroid property and which segment is the longer oneApollonius theorem relating a median to the three sidesRecognising a right angle inside a triangle that converts a length into Pythagoras

Common traps

Using the full medians 12 and 9 in Pythagoras, which gives 15 cm.
Splitting each median 1 : 2 from the vertex, which gives legs of 4 cm and 3 cm and an AB of 5 cm.
Adding AG and BG to 14 cm and forgetting that they are perpendicular.

The median also turns up as a property to recognise rather than a length to compute. 19 Sep 2024, 16:00, Quant Q.12 asks which statement about the median PT of triangle PQR is correct, and 23 Sep 2024, 12:30, Quant Q.6 asks what kind of triangle has equal medians.

In a numerical version like this one, the 2 : 1 split at the centroid is the line that has to come first — everything after it is plane Pythagoras.

Related PYQs

No directly related past PYQ was found.