In △XYZ , XZ=7 , YZ=7 , and XY=6 .
What is the area of the triangle?
Enter your answer, in simplified radical form, in the box.
This is an isosceles triangle.
Drop a perpendicular from Z to side XY; call the point of intersection P.
Since the triangle is isosceles, P will be the midpoint of side XY.
It is a right triangle.
Its hypotenuse is 7, one of its sides is 3.
Using the Pythagorean Theorem to find the other side: 32 + ZP2 = 72
---> 9 + ZP2 = 49 ---> ZP2 = 40 ---> ZP = sqrt(40) ---> ZP = 2 · sqrt(10)
The base of the triangle is XY; the height is ZP.
Its area is ½ · 6 · 2 sqrt(10) = 6 · sqrt(10)