Answer:
(D) 85 cm².
Explanation:
To find the area of a triangle, we can use the formula:
Area = (1/2) x base x height
In this case, we are given the lengths of three sides of the triangle, but we need to find the height. One way to do this is to use Heron's formula to calculate the area directly, but another approach is to use the Pythagorean theorem to find the height.
We can see that the side lengths of the triangle are 17 cm, 10 cm, and 9 cm. Let's assume that the side of length 17 cm is the base of the triangle. Then, we can draw an altitude from the vertex opposite the base to the base, creating two right triangles. The height of the triangle is the length of this altitude.
Using the Pythagorean theorem in one of the right triangles, we can solve for the height as follows:
(Height)^2 = (10 cm)^2 - (4.5 cm)^2
Height = sqrt[(10 cm)^2 - (4.5 cm)^2]
Height = sqrt[100 cm^2 - 20.25 cm^2]
Height = sqrt(79.75) cm
Height ≈ 8.93 cm
Now that we have the base and height of the triangle, we can use the formula for the area of a triangle:
Area = (1/2) x base x height
Area = (1/2) x 17 cm x 8.93 cm
Area ≈ 76.025 cm²
Therefore, the area of the triangle is approximately 76.025 cm². None of the answer choices match this result exactly, but the closest option is (D) 85 cm².