SSC CGL 2024 Tier-I · 10 September 2024, Shift 3 · Quantitative Aptitude · Question 21 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.

The area of a square is 16x² + 40x + 25 square units. Find the perimeter of the square.

Answer

Why

Correct — D. The area of a square is side², so the expression must be a perfect square.

16x² + 40x + 25
= (4x)² + 2·(4x)·5 + 5²
= (4x + 5)²

So the side is 4x + 5.

Perimeter = 4 × side = 4(4x + 5) = 16x + 20
Now match the printed forms: 2(8x + 10) = 16x + 20 → option (d).

Why the others are wrong

(a)
Expands to 24x + 30, which is 6(4x + 5) — six sides, not four. The multiplier for a square's perimeter is 4.
(b)
Expands to 30x + 24, the 10 and the 8 swapped. It is not a multiple of the side 4x + 5, so it cannot be this square's perimeter.
(c)
Expands to 20x + 16, which is 4(5x + 4) — the perimeter of a square of side 5x + 4. But (5x + 4)² = 25x² + 40x + 16, not the given area.

Concept

Two ideas meet here: area = side² for a square, and the perfect square trinomial a² + 2ab + b² = (a + b)².

Recognise the pattern from the ends. 16x² is (4x)² and 25 is 5², so if this is a perfect square its middle term must be 2 × 4x × 5 = 40x. It is, so the side is 4x + 5.

The perimeter follows as 4(4x + 5) = 16x + 20. SSC then prints that in a factored form you have to recognise.

Every option is written factored, and none of them reads 16x + 20 on its face.

Expand before you compare — 2(8x + 10) is the same expression. Matching an answer to a differently factored option is half the work in this item.

Key facts

16x² + 40x + 25 = (4x + 5)², because 2 × 4x × 5 = 40x matches the middle term.
A square of side s has area s² and perimeter 4s.
The perimeter here is 4(4x + 5) = 16x + 20, printed as 2(8x + 10).

Study next

Spotting a² − 2ab + b² and a² − b² inside mensuration stemsRectangle area that factorises into two distinct binomials, giving length and breadthTesting whether a quadratic is a perfect square using b² = 4ac

Common traps

Square-rooting only the first and last terms without checking the middle term.
Stopping at the side 4x + 5 when the question asks for the perimeter.
Not expanding the options and missing that 2(8x + 10) equals 16x + 20.

SSC wraps identity recognition inside a mensuration sentence, so the geometry is one line and the algebra is the real question.

The same shift tests the square identities in pure algebra at Quant Q.18, where x² + y² = 280 and xy = 120 have to become (x ± y)².

Related PYQs

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