A right triangle has sides of length 2 2, 6 2, and 80 units. What is the area of the triangle, in square units?
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. The area, A, of a triangle can be found using the formula =1 A bh, where b is the length of the base of the triangle and h is the height 2 of the triangle. It’s given that the triangle is a right triangle. Therefore, its base and height can be represented by the two legs. It’s also given that the triangle has sides of length 2 2, 6 2, and 80 units. Since 80 units is the greatest of these lengths, it’s the length of the hypotenuse. Therefore, the two legs have lengths 2 2 and 6 2 units. Substituting these values for b and h in the formula =1 =1 ( )( ) = A bh gives A 2 2 6 2 , which is equivalent to A 6 4 square units, or 2 2 = A 12 square units. Choice A is incorrect. This expression represents the perimeter, rather than the area, of the triangle. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.
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