Answer:
[tex]l=31\ cm\\\\w=24\ cm[/tex]
Step-by-step explanation:
The formula that is used to calculate the area of a rectangle is:
[tex]A=lw[/tex]
Where "l" is the lenght and "w" is the width.
You know that the area of that rectangle is:
[tex]A=744\ cm^2[/tex]
And, according to the exercise, its lenght is 7 more than its width; then:
[tex]l=w+7[/tex]
Then, you can make the corresponding substitution into the formula [tex]A=lw[/tex]:
[tex]744=(w+7)w[/tex]
Simplify:
[tex]744=w^2+7w\\\\w^2+7w-744=0[/tex]
Factor the equation. Find two numbers whose sum is 7 and whose product is -744. These are 31 and -24.
Then, you get:
[tex](w-24)(w+31)=0\\\\w_1=24\\\\w_2=-31[/tex]
The width of the rectangle is the positive value:
[tex]w=24\ cm[/tex]
Then, the lenght is:
[tex]l=24+7\\\\l=31\ cm[/tex]
