So, here we have that area is 10.26cm2.
We know that the equation to find area of a triangle is (bh)/2.
If we replace, we have:
A= (bh)/2, -----> 10.26=(bh)/2 -------> 20.52=bh (equation 1)
If we want to find "h", the best thing we can do here is to use Pythagoras theorem. Then, we got this equation:
8^2 - (2.7+x)^2= h^2
64 - (7.29 + 5.4x + x^2) = h^2
56.71 - 5.4x - x^2 = h^2 (equation 2)
where x is the rest of the side.
Now, we have two equations, right?
So we are going to find h in function of x.
If 20.52 = bh, then h=(b/20.52). But we know that b is equal to (2.7+x)
So the equation will be:
h=(2.7+x)/(20.52) (Equation 3).
If we equal equations 3 and 1:
h^2 = 56.71 - 5.4x - x^2 = h^2
And, h^2 = (7.29 + 5.4x + x^2)/421.0704 ( Applied (2.7+x)^2)
We have that h^2 = h^2, so
56.71 - 5.4x - x^2 =
Then we have a quadratic equation, and if we solve it, we obtain x=