The height of a television screen is 75% of its width. The screen is 20 inches wide. What is the area of the television screen.
By percent, how does this area compare to the area of a 20-inch by 20-inch screen?
The area of the television screen is _ square inches.
The area is _% of the area of a 20-inch by 20-inch screen.

Question

11-01-2018
Mathematics

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The height of a television screen is 75% of its width. The screen is 20 inches wide. What is the area of the television screen.
By percent, how does this area compare to the area of a 20-inch by 20-inch screen?
The area of the television screen is _ square inches.
The area is _% of the area of a 20-inch by 20-inch screen.

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JonHenderson55 JonHenderson55 · Answer 1 · 2018-01-14T11:31:41+01:00

Answers:
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Part 1) "The height of a television screen is 75% of its width. The screen is 20 inches wide. What is the area of the television screen?"

Answer: " The area of the television screen is:  " 300 in² " .
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Part 2) "By percent, how does this area compare to the area of a 20-inch by 20-inch screen?

Answer:   "The area of the [300 in²] television screen is "[tex] \frac{3}{16}[/tex]" % of [the area of a "20-inch by 20-in screen—which is: 400 in²] " .

{or, write as:

"The area of the [300 in²] television screen is "0.1875" % of the area of a 20-inch by 20-in screen."
_______________________________________________________
Explanation:
______________________________________________________
Part 1) "What is the area of the television screen"?

A = L * w ;

{"Area = Length * width"} . In this case, the "height" functionss as the "length".

A = w * (0.75)w ;

A = (0.75)*w² = (0.75)*(20 in)² = (0.75)*(20)² *(in²) ;

= (0.75) (20)(20)*(in²) ;

= (0.75)*(400)*(in²) ;

= (3/4)*(400)*(in²) ;

= 300 in² .

Answer: The area of the television screen is: " 300 in² " .
_______________________________________________________

Part 2) "By percent, how does this area compare to the area of a 20-inch by 20-inch screen?"

Note: The area of a "20-inch by 20-inch screen" equals: "400 in² " .

Explanation:

Area, "A" = (20 inches)² = (20)² * (in²) = (20)*(20)*(in²) = 400 in² .

So, "300 is what percent of 400" ? (300 is from our previous solved problem)?

300 = (n/100) * 400 ;

Divide each side by 400:

300/400 = { (n/100) * 400 } / 400 ;

3/4 = (n/100) * 400 ;

↔ (n/100) * 400 = 3/4;

→ 400n / 100 = 3/4 ;

→ 4n = 3/4 ;

Multiply each side of the equation by "1/4" ;

→ (1/4) * (4n) = (3/4) *(1/4) ;

→ n = 3/16 ; or write as: 0.1875

Answer:
"The area of the [300 in²] television screen is "[tex] \frac{3}{16}[/tex]" % of the area of a 20-inch by 20-in screen."

{or, write as:

"The area of the [300 in²] television screen is "0.1875" % of the area of a 20-inch by 20-in screen."
____________________________________________________