Hello!
We are given two sides of a right triangle.
If you notice the two sides, if divided by 5, fit the 3, 4, 5 right triangle formula, you could determine that AC is 15
But if not, or if you want to be sure, let's use the Pythagorean Theorem
\(a^2 + b^2 = c^2\)
\(20^2 + b^2 = 25^2\)
400 + \(b^2\) = 625
\(b^2\) = 225
b = 15
You don't have to learn all the squares from 1-100 but knowing popular ones like \(25^2\) and \(15^2\) is very useful
So now that we know that AC is indeed 15, how do we use this information?
The area of a triangle is \(\frac{1}{2}\)(base)(height)
In this case it is \(\frac{1}{2}\)(15)(20) = 15(10) = 150
Ok, so what?
Well, now you can use BC as the base and AD as the height and plug it into the equation to determine the length of AD
1/2(25)(AD) = 150
25(AD) = 300
AD = 12
The answer is (C)
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