Question

1. calculate the width of a 70” tv if the tv has an aspect ratio of 16:9.

80.33”
44.8”
39.4”
61”

Explanation:

Step1: Recall Pythagorean - related formula

For a TV with aspect ratio $16:9$, let the width be $16x$ and the height be $9x$. The diagonal $d$ of the TV screen is related to width and height by the Pythagorean theorem $d^{2}=(16x)^{2}+(9x)^{2}$. Given $d = 70$.

Step2: Simplify the equation

First, expand the right - hand side: $(16x)^{2}+(9x)^{2}=256x^{2}+81x^{2}=337x^{2}$. So, $337x^{2}=70^{2}=4900$.

Step3: Solve for $x$

$x^{2}=\frac{4900}{337}$, then $x=\sqrt{\frac{4900}{337}}\approx\sqrt{14.54}=3.81$.

Step4: Calculate the width

The width $w = 16x$. Substitute $x\approx3.81$ into it, $w = 16\times3.81 = 60.96\approx61$.

Answer:

61"