Q3 of 27 Page 84

An isosceles triangle has to be made like this


The height should be 2 metres less than the base. What should be the length of its sides?

If height is 2 m less than base


Let Base be x m


Then;


Height is (x–2)


In half of the triangle


⇒ By Pythagoras theorem:-


Base2 + Height2 = Side2


As in isosceles triangle


Altitude and median are the same


∴ in half of triangle


Base =


Height = (x–2)


Side is same as base because it is isosceles triangle


Side = x


Base2 + Height2 = Side2


= x2


+ x2 + 4–4x = x2


+ 4–4x = x2–x2 = 0


= 0


x2 + 16–16x = 0


As comparing eq to ax2 + bx + c = 0


x =


x =


The length cannot be negative


Hence Base is


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