SOLUTION: 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 measurm

Algebra ->  Finance -> SOLUTION: 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 measurm      Log On


   

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)
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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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)
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1.  Calculate the hypotenuse |BC| = sqrt%285%5E2+%2B+8%5E2%29 = sqrt%2825%2B64%29 = sqrt%2889%29.


2.  Calculate the area of the triangle S = %281%2F2%29%2A5%2A8 = 40 cm.


3.  You can express the area by another way: S = %281%2F2%29%2Aabs%28BC%29%2Aabs%28AD%29 = %281%2F2%29%2Asqrt%2889%29%2Aabs%28AD%29.


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

       %281%2F2%29%2Asqrt%2889%29%2Aabs%28AD%29 = 40,

    which gives you |AD| = %2840%2A2%29%2Fsqrt%2889%29 = 80%2Fsqrt%2889%29.

Solved.


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Comment from student: Thank you so much.One more thing please,what about mBD?
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My respense: O ! I expected this question.

|BD| = sqrt%28abs%28AB%29%5E2+-+abs%28AD%29%5E2%29.

Calculate it on your own !


Happy calculations !!