Question

if an area of an isosceles right angled triangle is 32 cm square. then the length of its longest altitude is equal to?

Answer 1

The triangle is a right angled isoceles triangle.

We know that for a right angle triangle,
$c^{2} = a^{2} + b^{2}$
where c is the hypotenuse, a and b are the sides

we know that this is an isosceles triangle,
which means that
a = b
So,
[tex] c^{2} = a^{2} + a^{2} [/tex]

or, $c = a \sqrt{2}$

Now, dump these values in heron's formula for area of a triangle
You will get the values of a,b,c
Either a or b will be the longest altitude of the triangle