Geometry

Quadrilaterals

Medium

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:

16 cm

6 cm

$8\sqrt{2}$ cm

8 cm

✅ Correct Option: 4

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

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CUET General Test Past Year Questions (Topic-Wise)

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: