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 #45 #. What are the lengths of sides A and B?

1 Answer
Binayaka C.
Oct 25, 2016

The length of sides #A and B# are #30.04(2dp) unit# each.

Explanation:

Here the Isocelles triangle have base #C=3# and the legs as sides #A and B#. The area is #A_t=45#
We know area of triangle as #A_t =1/2 * C . h# where h is altitude of the triangle. # 1/2*3*h=45 or h= 90/3=30#
In isocelles triangle altitude touches the base (C) at mid point (D) and is perpendicular to the base. So applying pythagorus theorem we get #A^2 =30^2+ (3/2)^2 or A=sqrt (900+2.25)=30.04(2dp)=B#

The length of sides #A and B# are #30.04(2dp) unit# each.[Ans]

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