Two corners of an isosceles triangle are at #(2 ,9 )# and #(8 ,3 )#. If the triangle's area is #9 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-23T12:41:56

The length of three sides of triangle are #8.49 ,4.74 , 4.74# unit

Base of the isocelles triangle is

#B= sqrt((x_1-x_2)^2+(y_1-y_2)^2)) = sqrt((2-8)^2+(9-3)^2)#

# =sqrt(36+36)=sqrt72 ~~8.49(2dp)#unit

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

is altitude. #:.9=1/2*8.49*H or H= 18/8.49~~2.12(2dp)#unit

Legs are #L = sqrt(H^2+(B/2)^2)= sqrt( 2.12^2+(8.49/2)^2)#

#=4.74(2dp)#unit.

The length of three sides of triangle are #8.49 ,4.74 , 4.74# unit [Ans]