Mathematics: The length of a rectangle is 7 more than the width the area is 744 square centimeters find length and width of rectangle

The answer is 3/4 and it was already simplified...

The length of a rectangle is 7 more than the width

cedricevans41p4j3kx

14.03.2022

$l=31\ cm\\\\w=24\ cm$

Step-by-step explanation:

The formula that is used to calculate the area of a rectangle is:

A=lw

Where "l" is the lenght and "w" is the width.

You know that the area of that rectangle is:

$A=744\ cm^2$

And, according to the exercise, its lenght is 7 more than its width; then:

l=w+7

Then, you can make the corresponding substitution into the formula A=lw :

744=(w+7)w

Simplify:

$744=w^2+7w\\\\w^2+7w-744=0$

Factor the equation. Find two numbers whose sum is 7 and whose product is -744. These are 31 and -24.

Then, you get:

$(w-24)(w+31)=0\\\\w_1=24\\\\w_2=-31$

The width of the rectangle is the positive value:

$w=24\ cm$

Then, the lenght is:

$l=24+7\\\\l=31\ cm$

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