Question 1066549
.
Triangle ABC is a right triangle with angle A = 90 degress.From the vertex A perpendicular AD is drawn on BC. 
If mAB = 5 cm, mAC = 8 cm. Find mBC, mAD and mBD. (m stands for measurment)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
1.  Calculate the hypotenuse |BC| = {{{sqrt(5^2 + 8^2)}}} = {{{sqrt(25+64)}}} = {{{sqrt(89)}}}.


2.  Calculate the area of the triangle S = {{{(1/2)*5*8}}} = 40 cm.


3.  You can express the area by another way: S = {{{(1/2)*abs(BC)*abs(AD)}}} = {{{(1/2)*sqrt(89)*abs(AD)}}}.


4.  Since the area is the same, you get the equation

       {{{(1/2)*sqrt(89)*abs(AD)}}} = 40,

    which gives you |AD| = {{{(40*2)/sqrt(89)}}} = {{{80/sqrt(89)}}}.
</pre>

Solved.



----------------------
<U>Comment from student</U>: Thank you so much.One more thing please,what about mBD?
----------------------



<U>My respense</U>:  O !   I expected this question.


|BD| = {{{sqrt(abs(AB)^2 - abs(AD)^2)}}}.


Calculate it on your own ! 



Happy calculations !!