Question

Find the area of a square if the sum of the diagonals is 100 cm.
(A) 100√2 cm²
(B) 1250 cm²
(C) 125 cm²
(D) 5000 cm²​

Answer 1

Answer:

Step-by-step explanation:

Given :

Sum of the diagonals = 100 cm

Procedure :

Let a be the side of the square and d be the diagonal of the square.

Formulae :

Area of a square = a² units²

Concept : Diagonals are equal in square and is equal to √2 × a. [Derivation in the attached picture]

As Sum of diagonals = 100 cm,

∴ One of the diagonal (d) = 50 cm.

As d = (√2 × a)

Squaring on both sides,

⇒ d² = 2a²

∴ a² = (d²/2)

As Area (A) = a²

∴ A = (1/2) × d²

Substitute d = 50 cm in the above equation.

⇒ A = (1/2) × (50)²

⇒ A = 2500/2

∴ A = 1250 cm²

Hence area of the square = 1250 cm².

Hence option (b) is the correct answer.

Thanks !