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 9 and the triangle has an area of 90 90. What are the lengths of sides A and B?

1 Answer
Shwetank Mauria
Jun 4, 2016

Lengths of side A and B are 20.520.5 units.

Explanation:

Let the sides A and B be aa units each. As side C has a length of 99 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)√a2−(92)2 and as area of triangle is 9090 units

sqrt(a^2-(9/2)^2)xx9/2=90√a2−(92)2×92=90

Hence sqrt(a^2-(9/2)^2)=90xx2/9=20√a2−(92)2=90×29=20

or a^2-(9/2)^2=400a2−(92)2=400

a^2=400+81/4=1681/4a2=400+814=16814

or a=41/2=20.5a=412=20.5

Lengths of side A and B are 20.520.5 units.

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