Question

The perimeter of an isosceles right triangle is 5(2+√2)cm. Its area is
(1) 5 cm²
(2) 10 cm²
(3) 12.5 cm²
(4) 25 cm²

I NEED THE STEPS ALSO!​

Answer 1

GIVEN: Isosceles Right triangle ABC right angled at B, AB = BC = a

So, hypotenuse AC = √(2a²) = √2a ( by Pythagoras law)

Hence, Perimeter = 2a +√2a

=> 2a + √2a = 5(2+√2)

=> a(2+√2) = 5 (2+√2)

=> a = 5

Hence area( triangle ABC) = (1/2) * BC * AB

=> area( tri ABC) = (1/2)*5*5 = 25/2 = 12.5

Area ( tri ABC) = 12.5 cm²

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