Two corners of an isosceles triangle are at #(2 ,9 )# and #(8 ,5 )#. If the triangle's area is #9 #, what are the lengths of the triangle's sides?

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Answer 1 · 2018-05-03T11:42:15

Length of three sides of the triangle are #7.21 ,4.39 , 4.39# unit

Base of the isosceles triangle is

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

#= sqrt((8-2)^2+(5-9)^2)) =sqrt(36+16)=sqrt 52 =7.21 (2dp)#

unit .We know area of triangle is #A_t =1/2*B*H#, where

#H# is altitude. #:. 9=1/2*7.21*H or H= 18/7.21= 2.50 (2dp)#

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

#= sqrt( 2.50^2+(7.21/2)^2)= 4.39 (2dp)#unit

Length of three sides of triangle are #7.21 ,4.39 , 4.39# unit [Ans]