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

Question

https://gmatclub.com/forum/download/file.php?id=61866 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 Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS 1.png

rajatchopra1994 · Answer

Explanation:

AC^2 = BC^2 - AB^2
AC^2 = 625 - 400
AC^2 = 225
AC = 15

1/2 × Base AC × Height AB = 1/2 × Base BC × Height AD
15 × 20 = 25 × Height AD
Height AD = 3×4 = 12

IMO-C

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sumitkrocks · Answer

Triangle ABC and DBA are similar

\frac{AD}{AC}  =  \frac{AB}{BC}  
AC =  \sqrt{(25^2-20^2)}  = 15 
 AD = 15*\frac{20}{25} =12

asishron29181 · Answer

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

kantapong · Answer

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)

HarshaBujji · Answer

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

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TarunKumar1234 · Answer

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.

PolarisTestPrep · Answer

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)

Showmeyaa · Answer

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!

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

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

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