Two corners of an isosceles triangle are at #(1 ,3 )# and #(5 ,8 )#. If the triangle's area is #8 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-15T15:36:22

The length of three sides of triangle are #6.40 ,4.06 , 4.06# unit.

Base of the isocelles triangle is

#B= sqrt((x_2-x_1)^2+(y_2-y_1)^2)) = sqrt((5-1)^2+(8-3)^2)) #

#=sqrt(16+25)=sqrt41 ~~ 6.40(2dp)#unit.

We know area of triangle is #A_t =1/2*B*H#

Where #H# is altitude.

#:. 8=1/2*6.40*H or H= 16/6.40 (2dp) ~~ 2.5#unit.

Legs are #L = sqrt(H^2+(B/2)^2)#

#= sqrt( 2.5^2+(6.40/2)^2)~~4.06(2dp)#unit

The length of three sides of triangle are #6.40 ,4.06 , 4.06# unit [Ans]