CUET UG 2025 — General Test Geometry

2025mcqmedium

The diagonal of a square is $4\sqrt{2}$ cm. The diagonal of another square whose area is double that of the first square, is:

Official previous-year question

Held on 16 May 2025 · Verified 13 Jul 2026.

Options

A
16 cm
B
6 cm
C
$8\sqrt{2}$ cm
D
8 cm

Did you get this right?

Solution

The diagonal of the first square is $4\sqrt{2}$ cm.

For any square with side length $a$ , the diagonal is $a\sqrt{2}$ and the area is $a^2$ .

Let the side of the first square be $a$ .

Diagonal = $a\sqrt{2}$

$4\sqrt{2} = a\sqrt{2}$

$a = \frac{4\sqrt{2}}{\sqrt{2}}$

$a = 4$ cm

Area of the first square:

Area = $a^2$

Area = $(4)^2$

Area = $16$ cm²

The second square has double the area:

Area of second square = $2 \times 16$

Area of second square = $32$ cm²

Let the side of the second square be $b$ .

$b^2 = 32$

$b = \sqrt{32}$

$b = \sqrt{16 \times 2}$

$b = 4\sqrt{2}$ cm

The diagonal of the second square:

Diagonal = $b\sqrt{2}$

Diagonal = $4\sqrt{2} \times \sqrt{2}$

Diagonal = $4 \times 2$

Diagonal = $8$ cm

The diagonal of the second square is $8$ cm.

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Solution

The diagonal of the first square is $4\sqrt{2}$ cm.

For any square with side length $a$ , the diagonal is $a\sqrt{2}$ and the area is $a^2$ .

Let the side of the first square be $a$ .

Diagonal = $a\sqrt{2}$

$4\sqrt{2} = a\sqrt{2}$

$a = \frac{4\sqrt{2}}{\sqrt{2}}$

$a = 4$ cm

Area of the first square:

Area = $a^2$

Area = $(4)^2$

Area = $16$ cm²

The second square has double the area:

Area of second square = $2 \times 16$

Area of second square = $32$ cm²

Let the side of the second square be $b$ .

$b^2 = 32$

$b = \sqrt{32}$

$b = \sqrt{16 \times 2}$

$b = 4\sqrt{2}$ cm

The diagonal of the second square:

Diagonal = $b\sqrt{2}$

Diagonal = $4\sqrt{2} \times \sqrt{2}$

Diagonal = $4 \times 2$

Diagonal = $8$ cm

The diagonal of the second square is $8$ cm.

CUET UG 2025 — General Test Geometry

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CUET UG 2025 — General Test Geometry

Options

Did you get this right?

Solution

Your note

CUET UG Geometry in other years

More CUET UG Geometry questions

Other General Test topics for CUET UG

General Knowledge

Logical Reasoning

Arithmetic

Quantitative Reasoning

Current Affairs

Keep practicing Geometry