in a right-anled triangle,sides are a,b and hypotenuse is c.if h is the altitude drawn on hypotenuse,then a- h*h=ab b- h*h=a*a+b*b c- h=a+b d- 1/h*h=1/a*a+1/b*B

Asked by architsrivastava02 | 4th Sep, 2010, 10:35: AM

Expert Answer:

Dear Student,
 
Let ABC be the right angled triangle with angle B=90o, AB = a; BC =b and AC =c. Let the altitude h meets AC at D. Let CD = x. So, DA = c-x
 
Hence;
In triangle BDC and ABD:
x2 = b2 - h2......................... (1)
     (c-x)2 = a2 - h2.....................(2)
Also,c2 = a2+b2..........................(3) (from right triangle ABC)
equation (2):
      c2 + x2 - 2cx = a2 - h2
=> a2+b2 +b2 - h2 - 2cx = a2 - h2 (from equations 1 and 3)
=> x2 = b4 / c2
Substituting it in equation 1 and using equation 3, we get:
 
1/h2 = 1/a2 + 1/b2
 
which is the option d
 
Regards Topperlearning.

Answered by  | 5th Sep, 2010, 10:48: PM

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