### Instruction: Find the area of a triangle with side lengths 8, 9, and 9.### Response: To find the area of a triangle, I need the base and the height.
Since the triangle has two equal sides, it must be isosceles, so I can use either one of them as the base.
I'll choose the base to be 8, and then draw a perpendicular line from the opposite vertex to the base, forming the height.
This splits the triangle into two right triangles, each with base 4 and hypotenuse 9.
I can use the Pythagorean theorem to find the height, which is the missing leg of either right triangle.
Let h be the height, then h^2 + 4^2 = 9^2.
Simplifying, I get h^2 = 65, so h = sqrt(65).
Now I have the base and the height of the original triangle, so I can use the formula for the area: A = (1/2)bh.
Plugging in the values, I get A = (1/2)(8)(sqrt(65)).