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

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

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Answer 1 · 2016-03-17T22:10:30

#A= sqrt(6^2+7^2) => A= 5sqrt(3) = B#

Explanation:

Given: Area of an isosceles triangle, #A_Delta =42; C = 14#
Required: Length of sides #A# and #B#:
Solution: #A_Delta = 1/2 C*h; C = 14; h= height#
#42=1/2 (14*h); h=6 # Now the height forms a right angle triangle with hypotenuse of #A# and sides of #h# and #C/2#. So you can use the Pythagoras Theorem:
#A^2= h^2+(C/2)^2# you know #h# and #C/2=7# solve of A
#A= sqrt(6^2+7^2) => A= 5sqrt(3) = B#

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

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Explanation:

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