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Test
Math
Domain
Geometry and Trigonometry
Skill
Area and volume
Difficulty
Hard
ID: 306264ab
Modded SAT Question Bank by Abdullah Mallik

A right triangle has sides of length 22, 62, and 80 units. What is the area of the triangle, in square units?

  1. 82+80

  2. 12

  3. 2480

  4. 24


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Correct Answer: B
Rationale

Choice B is correct. The area, A, of a triangle can be found using the formula A=12bh, 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’s also given that the triangle has sides of length 22, 62, 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 22 and 62 units. Substituting these values for b and h in the formula A=12bh gives A=122262, which is equivalent to A=64 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. 

Question Difficulty: Hard
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