Jerry is buying a new large screen television for his game room. He knows that the diagonal of the television measures 42.1 inches and the base is 34.3 inches. What is the area of the television? (round to nearest tenth)

Hi there. I'm going to answer using the methods I currently know - which means I'll answer it in two parts.

So, I'm going to use the Pythagorean theorem and the formula for the area of a triangle.

42.1² - 34.3² = 595.92

[tex] \sqrt{595.92} [/tex] = 24.41

Area of a triangle = [tex] \frac{bh}{2} [/tex]

[tex] \frac{(34.3)(24.41) }{2} [/tex] = 418.63

Cheers~

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jhonjez jhonjez · Answer 2 · 2019-09-30T22:55:59+02:00

Answer:

[tex]837\ in^{2}[/tex]

Step-by-step explanation:

Hello, I think I can help you with this

Step 1

use the Pythagorean theorem to find the height of the tv

According to P.T

[tex]base^{2} +height^{2} =diagonal^{2} \\replacing\\(34.3 in)^{2} +height^{2} =(42.1 in)^{2} \\isolate\ height\\height^{2} =(42.1 in)^{2}-(34.3 in)^{2} \\height=\sqrt{(42.1 in)^{2}-(34.3 in)^{2}} \\height=\sqrt{595.92 in^{2} } \\h=24.41\ inches\\[/tex]

Step 2

find the area of the tv(rectangle)

Area=base*height

[tex]Area=34.3\ inch*24.41\ inch\\Area=837\ in^{2}[/tex]

Have a great day