If AB=20 and BC=25, what is the length of AD in the figure above?

Given, AB=20 and BC=25
BC^2 = AB^2 + AC^2
625= 400 + AC^2
AC = 15

Now in the above figure,
Area of triangle ABC = 0.5 * AB * AC = 0.5 * BC * AC
20*15 = 25x
x= 12

AD=12
IMO C

AB = 20, BC = 25 => AC = 15
Area of triangle ABC = (1/2) x 20 x 15 = (1/2) x 25 x AD
Hence, AD = 3 x 4 = 12 (C)

Pythagores triplet.
3,4,5
5,12,13
15,20,25

etc...

So other side is 15;

AB x AC = BC x AD, Since right angle triagle.

So AD=12

IMO C

Posted from my mobile device

AC^2 = 25^2 - 20^2
or, AC^2 = 225 or, AC = 15.

AD/AC = AB/BC or, AD/15 = 20/25 or, AD = 12.

So, I think C.

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)

AC = \(\sqrt{25^2 - 20^2} = 15\)
Now, ABC and ADB are similar triangles:
So,\(\frac{AB}{BC} = \frac{AD}{AC}\)(Why? They would be in similar ratio)
AD = 15 * 20/25 = 12, (C) IMO!