Two corners of an isosceles triangle are at #(7 ,5 )# and #(3 ,9 )#. If the triangle's area is #6 #, what are the lengths of the triangle's sides?

Question

Two corners of an isosceles triangle are at #(7  ,5   )# and #(3   ,9   )#.  If the triangle's area is #6   #, what are the lengths of the triangle's sides?

Aaliyah Anderson · Accepted Answer

The length of three sides of triangle are #5.66 ,3.54 , 3.54# unit

Base of the isocelles triangle is #B= sqrt((x_2-x_1)^2+(y_2-y_1)^2)) = sqrt((3-7)^2+(9-5)^2)) =sqrt(16+16)=sqrt32 =5.66(2dp)#unit We know area of triangle is #A_t =1/2*B*H# Where #H# is altitude. #:. 6=1/2*5.66*H or H= 12/5.66=2.12(2dp)#unit Legs are #L = sqrt(H^2+(B/2)^2)= sqrt( 2.12^2+(5.66/2)^2)=3.54(2dp)#unit The length of three sides of triangle are #5.66 ,3.54 , 3.54# unit [Ans]

Sophia Alfred · Answer

undefined Given two corners of the isosceles triangle at (7, 5) and (3, 9), the third corner can be determined as the midpoint of the line connecting these two corners. Then, using the coordinates of the three corners, you can calculate the lengths of the triangle's sides using the distance formula. However, without knowing which side is the base and which two sides are equal, it is challenging to provide specific lengths for the sides of the triangle based solely on the given information. Therefore, additional clarification or constraints are needed to determine the lengths of the triangle's sides.