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.

Answers:
___________________________________________________
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?"

 " 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?

  "The area of the [300 in²] television screen is "" %  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 .

 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


 "The area of the [300 in²] television screen is "" %  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."
____________________________________________________