One angle is a right angle. The length of the side opposite the right angle is 21. The length of

Question

For the triangle shown, which expression represents the value of $a$ ?

Accepted Answer

Choice A is correct. For the right triangle shown, the lengths of the legs are a units and 6 units, and the length of the hypotenuse is 21 units. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Therefore, a 2 + 6 2 = 21 2 . Subtracting 6 2 from both sides of this equation yields a 2 = 21 2 - 6 2 . Taking the square root of both sides of this equation yields a = &#177; 21 2 - 6 2 . Since a is a length, a must be positive. Therefore, a = 21 2 - 6 2 . Thus, for the triangle shown, 21 2 - 6 2 represents the value of a . Choice B is incorrect. For the triangle shown, this expression represents the value of a 2 , not a . Choice C is incorrect and may result from conceptual errors. Choice D is incorrect and may result from conceptual errors.

Question one-an