Question

question 8
10 pts
g.gsr.6.3 (mc)
if a tv is advertised as 52 inches, that is actually the length of the diagonal line on the tv. if the length of that tv is 48 inches, what is the width of the tv?
round to the nearest tenth.
21 inches
19.2 inches
20 inches
70.8 inches
question 9
10 pts
g.gsr.6.3 (hc)

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the TV screen is a rectangle, and the diagonal, length, and width form a right triangle. We can use the Pythagorean theorem, which states that for a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, the diagonal \(c = 52\) inches (hypotenuse), the length \(a=48\) inches (one leg), and we need to find the width \(b\).

Step2: Rearrange the Pythagorean theorem to solve for \(b\)

From \(a^{2}+b^{2}=c^{2}\), we can solve for \(b\) as \(b=\sqrt{c^{2}-a^{2}}\).

Step3: Substitute the known values

Substitute \(c = 52\) and \(a = 48\) into the formula:

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Wait, let's check the calculation again. Wait, \(52^{2}=2704\) and \(48^{2}=2304\). Then \(52^{2}-48^{2}=2704 - 2304=400\). Then \(\sqrt{400} = 20\).

Answer:

C. 20 inches (assuming the options are labeled as A. 21 inches, B. 19.2 inches, C. 20 inches, D. 70.8 inches)