Question

In triangle ABC,angle c=90 and CD perpendicular to AB,CD=h,BC=a,CA=b,AB=c,prove that,1/h^2=1/a^2+1/b^2

Answer 1

Step-by-step explanation:

we can see that

since c²=a²+b²

c=√a²+b²...(1)

since area of triangle =1/2base×height

1/2×a×b=1/2×h×c

a×b=h×c

h²=a²b²/a²+b²...(from (1))

1/h²=(a²+b²)/a²b²

1/h²=b²/a²b² + a²/a²b²

1/h²=1/a² + 1/b²...hence proved