a length of a rectangle is 7 more than the width. the area is 588 square centimeters.

Question

find the length and width

Answer 1

The area of a rectangle is defined by length x width = area. Shortened as l x w = a.

a is defined by 588 cm^2. l is defined as w + 7. Thus giving us the equation 588 = w x (w + 7)

We can expand that into 588 = w² + 7w, which translates into w² + 7w - 588 = 0, a quadratic equation.

Knowing a quadratic equation is ax² + bx + c, which factors out into (ax + b)(cx + d), it's intermediate form being (ac)x² + (ad + bc)x + (bd), ac is 1, therefore a and c are both 1. d + b = 7 while d x b = -588. This means either d or b is negative.

Factoring out 588 gives us the roots 2, 2, 3, 7, 7. Through some simple logic we can assign a 7 to each factor and assign 4 to one, 3 to the other, giving us the factors 28 and 21. d + b = positive 7 so 28 is positive while 21 is negative.

The problem states l is 7 more than w, so l = 28 and w = 21.