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?

Question

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?

Autumn Armstrong · Accepted Answer

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]

Caroline Aucoin · Answer

undefined To find the lengths of the sides of the isosceles triangle, first, calculate the length of the base. Then, use the given area to determine the height of the triangle. Once you have the height, you can apply the Pythagorean theorem to find the lengths of the sides.

1. Calculate the length of the base using the distance formula between the given points (9, 6) and (4, 7).
2. Use the formula for the area of a triangle (Area = 0.5 * base * height) to find the height of the triangle.
3. Apply the Pythagorean theorem to find the lengths of the remaining sides of the triangle.

Following these steps, you can find the lengths of the sides of the isosceles triangle.