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

Dear Student,

 

Let ABC be the right angled triangle with angle B=90^o, 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.