Q88 of 131 Page 226

Area of an isosceles triangle is 48 cm2. If the altitudes corresponding to the base of the triangle is 8 cm, find the perimeter of the triangle.


Consider an isosceles ∆ABC with base BC, equal sides AB and BC.


We know that, Area of triangle = × b × h


48 = × BC × 8


∴ BC = 12 cm


In an isosceles triangle, the altitude divides base into half.


So, DC = = 6 cm


Applying Pythagoras theorem in ∆ADC,


(AD)2 + (DC)2 = (AC)2


(8)2 + (6)2 = (AC)2


(AC)2 = 64 + 36 = 100


AC =√100 = 10 cm


Now, AB = AC = 10 cm


Perimeter of ∆ABC = 10 + 10 + 12 = 32 cm


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