I'm not sure if this is the easiest way of doing this, but it surely work.
Let the base of the triangle be AB, and let CH be the height. Just for reference, we have
Moreover, let CH=y and BC=z
Now, AHC, CHB and ABC are all right triangles. If we write the pythagorean theorem for each of them, we have the following system
If we solve the first two equations for y squared, we have
And we can deduce
So that the third equation becomes
(we can't accept the negative root because negative lengths make no sense)
This is important because if you were to answer in complex fractions instead of its simplest form, you would have a tough time multiplying complex fractions together. You would get a HUGE denominator or numerator, which makes things difficult. It is important to write a fraction in its simplest form because of exactly that; making things simple. Would you rather multiply 64/132*64/132 or 1/2*1/2?
I have no clue how to solve this myself but i would recommend using photomath for tricky equations because it gives you a step by step tutorial for the problem
Solve by simplifying both sides of the equation, then isolating the variable.
Exact Form: a = 29/5
Decimal Form: a = 5.8
Mixed-Number Form: a = 5 4/5
Hope this helps!
Have a great day!
-4 7/8, -22/5, -4.25, -3, 1
