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

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Re: If AB=20 and BC=25, what is the length of AD in the figure above? [#permalink]
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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

IMO C
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Re: If AB=20 and BC=25, what is the length of AD in the figure above? [#permalink]
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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)
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Re: If AB=20 and BC=25, what is the length of AD in the figure above? [#permalink]
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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.

IMO C

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Re: If AB=20 and BC=25, what is the length of AD in the figure above? [#permalink]
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AC^2 = 25^2 - 20^2
or, AC^2 = 225 or, AC = 15.

So, I think C.
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Re: If AB=20 and BC=25, what is the length of AD in the figure above? [#permalink]
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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

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Re: If AB=20 and BC=25, what is the length of AD in the figure above? [#permalink]
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Bunuel wrote:

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

A. 6
B. 9.6
C. 12
D. 20
E. 24

Project PS Butler

Attachment:
1.png

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!
Re: If AB=20 and BC=25, what is the length of AD in the figure above? [#permalink]
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