If difference between one side #a# of a right angled triangle and hypotenuse #b# is #1#, what is its third side?

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Answer 1 · 2017-06-05T06:24:33

#sqrt(b+a)# cm

Let the third side of that triangle is #x# cm.

We know, In a right angled triangle, #"(hypotenuse)"^2 = (base)^2 +(height)^2#

Here, #b^2 = a^2 + x^2#

#rArr x^2 = b^2-a^2#

#rArr x^2 = (b+a)(b-a) # [ put (b-a) = 1]

#rArr x^2 = (b+a)*1#

#rArr x = sqrt(b+a)#

Hence third side is #sqrt(b+a)# cm