The question I asked before didn't show up properly so here is the equation again?

Question

hb/2=
h+b+(squareroot)h^2+b^2
This is supposed to be an equation for the area
equalling the perimeter of a right angled triangle.
I am trying to make 'h' the subject, but finding it a
bit confusing!

Answer 1

hb/2 = h+b+sqrt(h^2+b^2)
take h+b to the left

hb/2-(h+b) = sqrt(h^2+b^2)

square both sides

h^2b^2/4 + h^2+b^2 + 2hb - hb(h+b) = h^2+b^2
or h^2b^2/4 +2hb -hb(h+b) = 0

or h^2b^2+8hb-4hb(h+b) = 0

trivial solution is h = 0 ->b = 0 or b=0 ->h = 0 so h and b not 0

so devide

hb +8 -4(h+b) =0
this is equation of 2 variables so let us put h in terms of b

h(b-4) = 4b-8
h = (4b-8)/(b-4)
b has to be <2 for h to be positve

h = 4(b-2)/(4-b) and b < 2

Answer 2

Instead of a right angled triangle, imagine a rectangle with a base of b and a height of h. Then the area of the rectangle would simply be bh (b times h). If we now draw a straight line from the top right corner to the bottom left corner, we will have split the rectangle into two equal right angled triangles. The area of each of these triangles would be half the area of the rectangle, or bh/2. This diagonal line would, of course, be the hypotenuse of each of the right angled triangles which, as you have stated, is the square root of (h^2 + b^2).

Hope that helps.

Answer 3

It is easier to see if you call the threes sides of the right triangle a,b,and c where c is the hypotenuse of the right triangle and a and b are the two legs.
The area of a right triangle is equal to 1/2 the product of its legs. So area = ab/2

The perimeter of a right triangle is a+b+c.
But since c =sqrt(a^2+b^2) by the Pythagorean theorem, we have perimeter a+b+sqrt(a^2+b^2).

So if area = perimeter we have ab/2 = a+b+sqrt(a^2+b^2).
Now if you use b as the base and a as the altitude = h, then simply replace a by h and get bh/2 = b+h+sqrt(h^2+b^2).

Answer 4

Oh, I see. That makes a bit more sense.

The bit to the right of the equation is equal to the perimeter of a right angled triangle ie
h + b + square root(h squared + b squared)
where h and b are the two sides at right angles to each other.
hope this helps

Answer 5

I can make your equation look prettier: P = h + b + √(h² + b²). However, I don't think there is a pretty way to express this in terms of h. :)

Answer 6

y square root it?

its just h*b/2