Find the perimeter of an isosceles right triangle having an area of 100 cm2.
Answers
Answer: The perimeter is 48.28 cm.
Explanation: It is an isosceles triangle so its two sides will be equal. It is a right triangle also.
Let the perpendicular be x.
So, perpendicular= base= x
Area of triangle = 1/2 * Base * Height
100 cm² = 1/2*x*x
100cm² = 1/2 * x²
200cm² = x²
√200 = x
So, perpendicular = base = √200cm = 10√2 cm.
Noun find hypotenuse we will use Pythagoras theorem.
Hypotenuse² = Base² + Perpendicular ²
Hypotenuse² = (√200)² + (√200)²
= 200 + 200
= 400
Hypotenuse² = 400
Hypotenuse = √400
= 20 cm
So, perimeter = sum of all sides
= 10√2 + 10√2 + 20
= 20√2 + 20
= 40.28 cm
Therefore, perimeter of the triangle is 40.28 cm.
Hope it helps.
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