An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #9 # and the triangle has an area of #90 #. What are the lengths of sides A and B?

1 Answer
Shwetank Mauria
Jun 4, 2016

Lengths of side A and B are #20.5# units.

Explanation:

Let the sides A and B be #a# units each. As side C has a length of #9# units, one can draw a perpendicular from point opposite which divides the side C in two equal parts.

Hence, height of perpendicular using Pythagoras theorem will be

#sqrt(a^2-(9/2)^2)# and as area of triangle is #90# units

#sqrt(a^2-(9/2)^2)xx9/2=90#

Hence #sqrt(a^2-(9/2)^2)=90xx2/9=20#

or #a^2-(9/2)^2=400#

#a^2=400+81/4=1681/4#

or #a=41/2=20.5#

Lengths of side A and B are #20.5# units.

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