A right triangle has sides of length 2 2 , 6 2 , and 80 units. What is the area

Question

A right triangle has sides of length 2 2 , 6 2 , and 80 units. What is the area of the triangle, in square units?

Accepted Answer

Choice B is correct. The area, A , of a triangle can be found using the formula A = 1 2 b h , where b is the length of the base of the triangle and h is the height 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&rsquo;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 A = 1 2 b h gives A = 1 2 2 2 6 2 , which is equivalent to A = 6 4 square units, or 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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