Question

molly wants to find the length of the diagonal of her tv. the tv is 48 inches wide and 27 inches tall. molly set up the following equation to solve for the length of the diagonal: (27)² + (48)² = c². did molly set up the equation correctly? explain your reasoning. molly set up the equation incorrectly. she doesnt need to square the length of the legs of the right triangle: 48 + 27 = c². molly set up the equation incorrectly. the diagonal of the tv is one leg of the right triangle she needs to use, so her equation should be (27)² + b² = (48)².

Explanation:

1. Identify the shape and theorem: The TV is a rectangle. When we draw a diagonal in a rectangle, it forms a right - triangle with the length and width (or height and width) of the rectangle. The Pythagorean theorem, which applies to right - triangles, states that for a right - triangle with legs of length \(a\) and \(b\) and hypotenuse of length \(c\), \(a^{2}+b^{2}=c^{2}\).
2. Apply the theorem to the TV: In this case, the width of the TV (\(48\) inches) and the height of the TV (\(27\) inches) are the legs (\(a = 27\), \(b = 48\)) of the right - triangle, and the diagonal of the TV is the hypotenuse (\(c\)). So according to the Pythagorean theorem, the equation should be \((27)^{2}+(48)^{2}=c^{2}\), which is exactly the equation Molly set up.
3. Evaluate the given options:

• The first option suggests using \(48 + 27=c^{2}\), which is incorrect because the Pythagorean theorem requires squaring the legs, not just adding their lengths.
• The second option suggests that the diagonal is a leg of the right - triangle, which is incorrect. The diagonal is the hypotenuse as it is opposite the right - angle formed by the width and height of the TV.

Answer:

Molly set up the equation correctly. (Note: Wait, actually, let's re - evaluate. Wait, the TV is a rectangle, and the diagonal forms a right triangle with the width and height. The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs (width and height) and \(c\) is the hypotenuse (diagonal). So Molly's equation \((27)^{2}+(48)^{2}=c^{2}\) is correct. But the options given seem to be wrong. Wait, maybe I misread the options. Wait, the first option says she should do \(48 + 27=c^{2}\), which is wrong. The second option says the diagonal is a leg, which is also wrong. Wait, maybe the question is a trick question where the options are wrong, but according to the Pythagorean theorem, Molly's setup is correct. But since the options are presented, maybe there's a mistake in the problem's options. But based on the Pythagorean theorem, the correct statement is that Molly set up the equation correctly because the TV's diagonal, width, and height form a right - triangle, and the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(a = 27\), \(b = 48\), and \(c\) is the diagonal) is applied correctly. However, if we have to choose from the given options, both options are incorrect. But maybe the original problem has a different intention. Wait, perhaps I made a mistake. Let's re - check: The TV is a rectangle, so length and width (or height and width) are the legs, diagonal is hypotenuse. So \(27^{2}+48^{2}=c^{2}\) is correct. So the answer is that Molly set up the equation correctly, and the given options are incorrect. But since the user provided the options, maybe there's a misprint. But according to the mathematical principle, Molly's equation is correct.