Find the perimeter of an isosceles right angled triangle having an area of metre square.
Step 1: Calculate the length of the sides
Given that an isosceles right-angled triangle of area .
Let us assume that the length of the equal side of the triangle is .
Since, the hypotenuse is the largest side in a right-angled triangle so both the equal sides are perpendicular to each other.
We know that area of a triangle is given by
where, is the base of the triangle and is the height of the triangle.
Substituting the given area values in the above equation, we get
Step 2: Calculate the hypotenuse
Since, it is the right-angled triangle we will find the hypotenuse using the Pythagoras theorem.
Hypotenuse
We know that
Hence, the two sides are and the hypotenuse is
Step 3: Calculate the perimeter
Perimeter of a triangle sum of all the three sides
Perimeter
Hence, the perimeter of the given isosceles right-angled triangle is .