Question

22. If the square of the hypotenuse of an isosceles right triangle is 200 m² Find its perimeter and area.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

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Solution:

Given that, it is a right angled isosceles triangle. So it means that the sides other than hypotenuse are equal in measure.

So let the side be denoted as 'x'

Now Area of triangle is given as 200 cm²

So Area of triangle = 1/2 * Base * Height

=> Area = 1/2 * x * x

=> Area = 1/2 * x² = x²/2

=> x²/2 = 200 cm²

=> x² = 200 × 2 = 400 cm²

=> x = √400 = 20 cm

So Applying Pythagoras Theorem we get,

=> x² + x² = Hypotenuse²

=> 20² + 20² = Hypotenuse²

=> 400 + 400 = Hypotenuse²

=> 800 = Hypotenuse²

=> Hypotenuse = √800 = 20√2 cm

Hence the side of the hypotenuse is 20√2 cm

Hope my answer helped !