Question

The pertmeter of a right angled isosceles triangle is 2p cm. What is its area?

विकल्प

• `(3 + 2sqrt(2))` p cm²

• `(3 - 2sqrt(2))` p cm²

• `(2 - sqrt(2))` p cm²

• `(2 + sqrt(2))` p cm²

Answer 1

`(3 - 2sqrt(2))` p cm²

Explanation:

AB = BC = x cm

∴ `2x + sqrt(2x) = 2p`

⇒ `x(2 + sqrt(2)) = 2p`

⇒ `x = (2p)/(2 + sqrt(2))`

= `(2p)/(2 + sqrt(2)) xx (2 - sqrt(2))/(2 - sqrt(2))`

= `(2p(2 - sqrt(2)))/(4 - 2)`

= `p(2 - sqrt(2))`

∴ Area of ΔABC = `1/2` AB × BC

= `1/2 x^2 = 1/2 p^2 (2 - sqrt(2))^2`

= `1/2 * p^2 (4 + 2 - 4sqrt(2))`

= `(3 - 2sqrt(2))p^2` sq.cm