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 #3 # and the triangle has an area of #42 #. What are the lengths of sides A and B?

1 Answer
[eden] · Shwetank Mauria
May 4, 2017

If we presume that C is the base of the triangle:

A = 28.04
B = 28.04

Explanation:

First we need to find the height or #h# of the triangle. We do this by using simple/basic algebra. In this case side C = #b#

= #(b*h)/2#
= #(3*h)/2 = 42#
= #(3*h) = 84#
= #h = 84/3#
= #28#

Then we use one of the most powerful tools in geometry to decode the side lengths of A and B, the Pythagoras Theorem. In this case, as A and B meet at the vertex and a perpendicular drawn from this point on base bisects it. Hence, it forms a right angled triangle, whose two legs are #h=28# and #3/2# (say #a# and #b#) and one of the equal side forms hypotenuse or #c#. And then we have

#a^2 + b^2 = c^2#
= #(3/2)^2 + 28^2 = c^2#
= #2.25 + 784 = c^2#
= #786.25 = c^2#
= #sqrt 786.25#
#approx# #28.04#

All the best!

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