Answer :

According to the question the perimeter of the rectangle must be always equal to 100 cm.

Now, let one side be x cm and other adjacent side be y cm.

⇒ P = 2 × [x + y]

⇒ 100 = 2x + 2y

⇒ y = 50 – x – (1)

(i) a(x) = (50-x) × (x) – (by (1))

a(x) = 50x – x^{2}

(ii) a(10) = 50 × (10) – (10)^{2} = 400

a(40) = 50 × (40) – (40)^{2} = 400

Now if a side a is 10 cm, then the other side

P = (10 + y) × 2

P = 100

⇒ 50 – 10 = y

⇒ y = 40 cm

∴ the in case of x = 10 cm y = 40 cm, and in case of x = 40 cm y = 10 cm. So, in both cases we have same rectangle hence the area is same.

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