In a right triangle, the area equals one-half the product of the lengths of which sides?

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Multiple Choice

In a right triangle, the area equals one-half the product of the lengths of which sides?

The area of a triangle is one-half times the base times the height. In a right triangle, the two legs meet at a right angle, so they are perpendicular. If you take one leg as the base and the other leg as the height, you’re using a perpendicular pair, and the area becomes (1/2) × (length of one leg) × (length of the other leg). That product is precisely the area, so the correct pair is the two legs that form the right angle. The hypotenuse isn’t perpendicular to a leg, and “any two sides” wouldn’t guarantee perpendicularity, so they wouldn’t necessarily give the area in that simple base×height form.

The area of a triangle is one-half times the base times the height. In a right triangle, the two legs meet at a right angle, so they are perpendicular. If you take one leg as the base and the other leg as the height, you’re using a perpendicular pair, and the area becomes (1/2) × (length of one leg) × (length of the other leg). That product is precisely the area, so the correct pair is the two legs that form the right angle. The hypotenuse isn’t perpendicular to a leg, and “any two sides” wouldn’t guarantee perpendicularity, so they wouldn’t necessarily give the area in that simple base×height form.

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