Two corners of an isosceles triangle are at #(7 ,2 )# and #(4 ,9 )#. If the triangle's area is #24 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-10-26T11:27:12

The length of three sides of triangle are #7.62 ,7.36 , 7.36# unit

Base of the isocelles triangle is #B= sqrt((x_1-x_2)^2+(y_1-y_2)^2)) #

# = sqrt((7-4)^2+(2-9)^2)) =sqrt(9+49)=sqrt58 ~~7.62(2dp)#unit

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

#:. 24=1/2*7.62*H or H~~ 48/7.62 ~~ 6.30(2dp) # unit

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

#= sqrt( 6.30^2+(7.62/2)^2) ~~7.36(2dp) # unit

The length of three sides of triangle are #7.62 ,7.36 , 7.36# unit [Ans]