Question

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

Answer 1

Answer:

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

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:

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