Question

A right-angled triangle has an area of 6 and its longest side is 5. Find the perimeter.

Answer 1

One equation we can derive the situation is this:
1/2 * b * h = 6
b * h = 12.

Another equation we can get is this :
b^2 + h^2 = 25 (This is a right triangle and thus the Pythagorean
theorem can be utilized)

Now, let's see what we are trying to find. The problem is asking for the perimeter of the triangle so essentially we want to find the value of: b + h + 5.
We are just in luck!

So far we know that:
b*h = 12 and b^2 + h^2 = 25
Something looks familiar...very familiar. And that is we can manipulate the two formulas into b^2+2bh+h^2! This can be factored into (b+h)^2. We know bh = 12, so 2bh must equal 24. So if we add 2bh to b^2 + h^2 = 25, we obtain b^2+2bh+h^2 = 49.
Then, we factor and get (b+h)^2 = 49. Taking the square root of both sides we obtain b+h = plus or minus 7. (we throw out minus 7 as we are talking about distance here)
So we have found b+h. Our goal was to find b+h+5, we plug b+h in and get 7 + 5 , which results in 12.


THUS, (PHEW), THE PERIMTER OF THE TRIANGLE IS 12!

Answer 2

thanks so much you've been a big help!

Answer 3

NP, could i have a medal please? lol

Answer 4

how do i send you one?