Question

A rectangle has an area of 60 cm2. Its width is 7 cm less than its length. (a) Let x cm be the length of the rectangle. Write an equation using the rectangle's area. (b) Solve your equation for x (c) Find the dimensions of the rectangle.

Answer 1

Answer: (a) $A = x^{2}-7x$

              (b) x = 12 or x = -5

              (c) Length = 12cm

                   Width = 5cm

Step-by-step explanation: Area of a rectangle is calculated as:

A = length*width

(a) If length = x,

width = x - 7

Then, equation is:

A = x(x - 7)

$A = x^{2} - 7x$

(b) Solving for x:

$A = x^{2} - 7x$

$x^{2} - 7x = 60$

$x^{2} - 7x - 60=0$

Using Bhaskara to solve equation:

$x = \frac{7+\sqrt{(-7)^{2}-4.1.(-60)} }{2}$

$x =\frac{7+\sqrt{289} }{2}$

$x =\frac{7+17}{2}$

$x_{1} = \frac{7+17}{2}$ = 12

$x_{2}=\frac{7-17}{2}$ = -5

The quadratic equation gives two values for x: x = 12 or x = -5

(c) Dimensions are positive numbers, so the value of x used is x = 12.

As length is x:

length = 12cm

Width is 7 less than length:

width = x - 7

width = 5cm

The rectangle has length of 12cm and width of 5cm.