Two corners of an isosceles triangle are at #(5 ,8 )# and #(9 ,1 )#. If the triangle's area is #36 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-01-06T11:09:11

The length of three sides of triangle are #8.06 ,9.8 , 9.8# unit

Base of the isocelles triangle is #B= sqrt((x_2-x_1)^2+(y_2-y_1)^2)) = sqrt((9-5)^2+(1-8)^2)) =sqrt(16+49)=sqrt65 =8.06(2dp)#unit

We know area of triangle is #A_t =1/2*B*H# Where #H# is altitude.
#:. 36=1/2*8.06*H or H= 72/8.06=8.93(2dp)#unit

Legs are #L = sqrt(H^2+(B/2)^2)= sqrt( 8.93^2+(8.06/2)^2)=9.80(2dp)#unit

The length of three sides of triangle are #8.06 ,9.8 , 9.8# unit [Ans]