Two corners of an isosceles triangle are at #(7 ,5 )# and #(3 ,9 )#. If the triangle's area is #6 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-07-21T11:01:34

The length of three sides of triangle are #5.66 ,3.54 , 3.54# unit

Base of the isocelles triangle is #B= sqrt((x_2-x_1)^2+(y_2-y_1)^2)) = sqrt((3-7)^2+(9-5)^2)) =sqrt(16+16)=sqrt32 =5.66(2dp)#unit

We know area of triangle is #A_t =1/2*B*H# Where #H# is altitude.
#:. 6=1/2*5.66*H or H= 12/5.66=2.12(2dp)#unit

Legs are #L = sqrt(H^2+(B/2)^2)= sqrt( 2.12^2+(5.66/2)^2)=3.54(2dp)#unit

The length of three sides of triangle are #5.66 ,3.54 , 3.54# unit [Ans]