SSC CGL 2024 Tier-I · 26 September 2024, Shift 3 · Quantitative Aptitude · Question 18 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 10 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.

If the altitude from two vertices of a triangle to the opposite sides are equal, then the triangle will be:

(a)equilateral triangle
(b)isosceles triangle
(c)scalene triangle
(d)obtuse angle triangle

Answer

Why

Correct — B. Call the triangle ABC and let the altitudes drawn from B and from C be equal.

Take AC as the base: Area = ½ × AC × h(from B)
Take AB as the base: Area = ½ × AB × h(from C)

A triangle has one area, so ½ × AC × h(from B) = ½ × AB × h(from C).
With the two altitudes equal, everything else cancels and AC = AB.

Two equal sides is the definition of an isosceles triangle → option (b).

Why the others are wrong

(a)
equilateral triangle — An equilateral triangle does satisfy the condition, but it is a special case, not what the condition forces. Equal altitudes from two vertices fix two sides only — the third is free to be any length the triangle allows.
(c)
scalene triangle — A scalene triangle has no two sides equal, so by Area = ½ × base × altitude its three altitudes are all different. It is precisely the shape the equal-altitude condition rules out.
(d)
obtuse angle triangle — The condition constrains sides, not angles. An isosceles triangle may be acute, right-angled or obtuse, so nothing here makes the triangle obtuse-angled.

Concept

Every triangle has a single area, and you may compute it from any side taken as the base: Area = ½ × base × altitude to that base.

That makes base and altitude inversely proportional inside one triangle — the longer the side you stand on, the shorter the altitude dropped onto it.

So two equal altitudes force the two sides they fall on to be equal, which is the isosceles condition. The statement reverses too: in an isosceles triangle the altitudes to the two equal sides are equal.

Isosceles here means at least two sides equal, and an equilateral triangle meets that description as well.

The question asks what the triangle must be, so the answer is the weakest description that always holds — isosceles, because nothing in the data can force the third side to join in.

Key facts

Area = ½ × base × altitude holds for all three sides of a triangle, so the product base × altitude is the same whichever side you choose.
Equal altitudes to two sides make those two sides equal.
The converse also holds: in an isosceles triangle the altitudes drawn to the two equal sides are equal.

Study next

Altitudes, medians and angle bisectors, and which of them coincide in an isosceles triangleProving triangle properties from the area formula instead of from congruenceThe equal-medians result, which forces an equilateral triangle rather than an isosceles one

Common traps

Choosing equilateral because all its altitudes are equal, when the data fixes only two of them.
Confusing altitude with median — the equal-medians version of this statement has a different answer.
Reading the equality as one about angles, and picking a description of the angles instead.

SSC states the property in one line, with no figure, and asks for the class of triangle. The equal-medians twin of this item is set at 23 Sep 2024, 12:30, Quant Q.6, where the keyed answer is equilateral.

Related PYQs

No directly related past PYQ was found.