Two corners of an isosceles triangle are at #(4 ,8 )# and #(5 ,7 )#. If the triangle's area is #5 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-09-16T11:47:01

The length of three sides of triangle are #1.41 ,7.11 , 7.11# unit.

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

# = sqrt((5-4)^2+(7-8)^2)) =sqrt(1+1)=sqrt2 ~~ 1.41(2dp) #unit

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

#:. 5=1/2*1.41*H or H= 10/1.41 ~~7.07(2dp)#unit

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

#= sqrt( 7.07^2+(1.41/2)^2) ~~7.11 (2dp)#unit

The length of three sides of triangle are #1.41 ,7.11 , 7.11# unit [Ans]