Two corners of an isosceles triangle are at #(9 ,6 )# and #(4 ,7 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-09-28T11:08:20

The length of three sides of triangle are #5.1 ,25.2 , 25.2# unit.

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

#= sqrt((9-4)^2+(6-7)^2)) =sqrt(25+1)=sqrt26 =5.1 (1dp)# unit

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

#:. 64=1/2*5.1*H or H= 128/5.1=25.1 (1dp)#unit

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

#= sqrt( 25.1^2+(5.1/2)^2)=25.2(1dp)#unit

The length of three sides of triangle are #5.1 ,25.2 , 25.2# unit [Ans]