Question

Find the perimeter of an isosceles right triangle having an area of 100cm

Answer 1

this is the solutions
you may check it and then tell me id it correct ot not

Answer 2

Answer:

48.28 cm

Step-by-step explanation:

We are given an isosceles right angled triangle .

Since it is an isosceles triangle .So, its two sides must be equal

Since it is a right angles triangle So, the two sides that must be equal are Perpendicular and Base.

Let the perpendicular be x

So, perpendicular = base =x

Area of triangle =$\frac{1}{2} \times base \times height$

Since we are given that the area is 100 sq.cm

So, $100=\frac{1}{2} \times x \times x$

$200=x^2$

$\sqrt{200}=x$

So, perpendicular = base = √200 cm = 10√2 cm

Now to find hypotenuse we will use Pythagoras theorem:

$Hypotenuse^2=Perpendicular^2+Base^2$

$Hypotenuse^2=(\sqrt{200})^2+(\sqrt{200})^2$

$Hypotenuse^2=200+200$

$Hypotenuse^2=400$

$Hypotenuse=\sqrt{400}$

$Hypotenuse=20$

So, perimeter = Sum of all sides

                      =$10\sqrt{2}+10\sqrt{2}+20$

                      =$20\sqrt{2}+20$

                      =$48.28cm$

Hence the perimeter of triangle is 48.28 cm