Question

if the area of an isosceles right angle triangle is 32cm then the lenth 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}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,
c^{2} = a^{2} + a^{2}c​2​​=a​2​​+a​2​​ 

or, c = a \sqrt{2}c=a√​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

Answer 2

The hypotenuse will be longest side nd it's measure will be 10.5cm.
Hope it will help u.
I also attached a pic with it