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If the diagonal of a rectangle is 10 cm long, and if it is double of a side of that rectangle, what is the area of the rectangle?
1. 100 cm2
2. 25\(\sqrt{3}\)  cm2
3. 25 cm2
4. 10\(\sqrt{3}\)  cm2

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Correct Answer - Option 2 : 25\(\sqrt{3}\)  cm2

Given:

The length of the diagonal of the rectangle is 10 cm. And if it is double of a side of that rectangle

Concept Used:

Area = Length × Breadth

Diagonal2 = Length2 + Breadth2

Calculation:

Length of the diagonal = 10 cm

Accordingly,

Length of one side of the rectangle = 10/2 = 5 cm

Let, length of another side be x

102 = 52 + x2

⇒ x2 = 100 - 25

⇒ x = √75

⇒ x = 5√3

Area of the rectangle = 5 × 5√3 = 25√3

∴ The area of the rectangle is 25√3 cm2.

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