Find the perimeter of an isosceles right angled triangle having an area of 5000 metre square.

Given that

A right-angle isosceles triangle of area 5000m2

We need to find the perimeter of the given isosceles triangle

Let us assume that the length of the equal side of the triangle be x

We know that area of a traingle is given by

Area = 1/2 x base x height

Substituting the given area values in the above equation, we get

5000 = 1/2 (x) (x)

1/2 x² = 5000

x² = 5000 x 2

x² = 10,000

x = √10000

x = 100

Since it is the right-angled triangle

we will find the hypotenuse using the Pythagoras theorem

hypotenuse = side(√2)

hypotenuse = 100√2

We know that √2= 1.41

hypotenuse= 100(1.41)= 141cm

Hence the two sides are 100cm and hypotenuse is 141cm

Perimeter of a triangle= sum of all the three sides

Perimeter = 100 + 100 + 141

Perimeter = 341 m

The perimeter of the given right-angled isosceles triangle is 341 m

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