Question

A television has a width: height ratio of 9:5. if the television is advertised as having a 36-inch screen (remember the screen is measured as the diagonal), what is the actual height and width of the television? what is the surface area of the screen?

Answer 1

Answer:

See below for answers and explanations

Step-by-step explanation:

Find the diagonal of a TV with a width : height ratio of 9:5

$9^2+5^2=c^2\\\\81+25=c^2\\\\106=c^2\\\\c=\sqrt{106}$

Divide 36 by this result to get the scale factor

$\displaystyle \frac{36}{\sqrt{106}}=\frac{36\sqrt{106}}{106}=\frac{18\sqrt{106}}{53}$

Multiply both the width and height by the scale factor

Actual width: $\displaystyle 9*\frac{18\sqrt{106}}{53}=\frac{162\sqrt{106}}{53}\approx31.47\:\text{inches}$

Actual height:  $\displaystyle 5*\frac{18\sqrt{106}}{53}=\frac{90\sqrt{106}}{53}\approx17.48\:\text{inches}$

Multiply the new width and height to find the surface area of the screen

$\displaystyle \frac{162\sqrt{106}}{53}*\frac{90\sqrt{106}}{53}=\frac{14580(106)}{2809}=\frac{1545480}{2809}\approx550.189\: \text{square inches}$