One angle is a right angle.

The lengths of the sides adjacent to the right angle are as follows:

3

7

A note indies the figure is not drawn to scale.

Question

The lengths of the legs of a right triangle are shown. Which of the following is closest to the length of the triangle's hypotenuse?

Accepted Answer

Choice C is correct. The Pythagorean theorem states that for a right triangle, a 2 + b 2 = c 2 , where a and b represent the lengths of the legs of the triangle and c represents the length of its hypotenuse. In the triangle shown, the legs have lengths of 3 and 7 . Substituting 3 for a and 7 for b in the equation a 2 + b 2 = c 2 yields 3 2 + 7 2 = c 2 , which is equivalent to 9 + 49 = c 2 , or 58 = c 2 . Taking the positive square root of both sides of this equation yields 58 = c . Thus, the value of c is approximately 7.6 . Therefore, of the given choices, 7.6 is the closest to the length of the triangle's hypotenuse. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question one-an