Mathematics, 28.07.2019 01:20 zombieslayas8500

The length of a rectangle is twice its width. find its area, if its perimeter is 7 1/3 cm.

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" 2.989 cm² " .
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Explanation:
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Let "A" represent the "area" ;
"L" represent the "Length" ;
"w" represent the "width" ;
"P" represent the "Perimeter".
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Note the following equations /formulas for a rectangle:

A = L * w ;
P = 2L + 2w ;

Given: "L = 2w " ;
and: " P = 7 $\frac{1}{3}$ cm" ; Solve for "A" ;
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7 $\frac{1}{3}$ cm = 2L + 2w ;

Divide EACH side by "2" ;
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7 $\frac{1}{3}$ cm / 2 = (2L + 2w) / 2 ;

to get:

7 $\frac{1}{3}$ cm / 2 = L + w ;

Given: L = 2w ; rewrite the above equation; substituting "2w" for "L" ;
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7 $\frac{1}{3}$ cm / 2 = 2w + w ;

7 $\frac{1}{3}$ cm / 2 = 3w ;
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Note:
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7 $\frac{1}{3}$ cm / 2 ;

= $\frac{[(3*7) + 1]}{3}$ cm / 2 ;

= $\frac{22}{3}$ cm / 2 ;

= $\frac{22 cm}{3}$ * $\frac{1}{2}$ ;

Note: The "22 cm" cancels to "11 cm" ; and the "2" cancels out to "1" ;

{Since: "(22 cm ÷ 2 = 11 cm)" ; and since: "(2 ÷ 2 = 1)" .

And we can rewrite the expression as:
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$\frac{11 cm}{3}$ * $\frac{1}{1}$ ;

and further simplify:

$\frac{11 cm}{3}$ * $\frac{1}{1}$ ;

=   $\frac{11 cm}{3}$ * 1 ;

=   $\frac{11 cm}{3}$ ;
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Now, we can take the equation:

7 $\frac{1}{3}$ cm / 2 = 3w ;
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and rewrite as:
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$\frac{11 cm}{3}$ = 3w ;

and multiply each side by " $\frac{1}{3}$ " ; to isolate "w" on one side of the equation ; and to solve for "w" ;

$\frac{11 cm}{3}$ * $\frac{1}{3}$ = {3w} * $\frac{1}{3}$ ;

to get:

   $\frac{11 cm * 1}{3*3}$ = w ;

   $\frac{11 cm}{9}$ = w ;

↔ w = $\frac{11}{9}$ cm ;
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Given: L = 2w ;

L = 2 * $\frac{11}{9}$ cm ;

L = { $\frac{2}{1}$ * $\frac{11}{9}$ } cm ;

L = $\frac{2*11}{1*9}$ cm ;

L = $\frac{22}{9}$ cm ;
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Now, solve for "A" (area):

A = L * w ;

A = $\frac{22}{9}$ cm * $\frac{11}{9}$ cm ;

A = $\frac{22* 11}{9*9}$ cm² ;

A = $\frac{242}{81}
$ cm² ;

A = 2.9876543209876543 cm² ; round to: "2.989 cm² " .
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Answer from: Quest

she was supposed to add the hours(38.5) and multiply the amount of money she earned(7.50) resulting in $288.75 .

correct me if i'm wrong and if it is i'm truly sorry.

Answer from: Quest

step-by-step explanation: sorry if not correct becaude my brother is loud and i could not think!

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