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

Accepted Solution

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]: Β [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]