Question

The length of a rectangle is 5 inches more than its width, x. The area of a rectangle can be represented by the equation x 2 + 5x = 300. What are the measures of the width and the length? Width = a0 inches Length = a1 inches

Answer 1

Answer:

Width = 15 inches             Length = 20 inches

Step-by-step explanation:

The area of a rectangle is calculated using the following formula.

$A = Lx$   (1)

Where L is the length and x is the width of the rectangle

In this case we know that the length of the rectangle is 5 inches greater than its width. This means that:

$L = x + 5$   (2)

Also The area of a rectangle can be represented by the equation $x^2 + 5x = 300$

so to find the width x we solve the equation

$x^2 + 5x -300=0$   (3)

For an equation of the form $ax ^ 2 + bx + c = 0$ the quadratic formula is:

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

In this case note that:

$a=1\\b=5\\c=-300$

Then:

$x=\frac{-5\±\sqrt{(5)^2-4(1)(-300)}}{2(1)}$

$x=\frac{-5\±\sqrt{25+1200}}{2}$

$x=\frac{-5\±\sqrt{1225}}{2}$

$x=\frac{-5\±35}{2}$

$x_1=\frac{-5+35}{2}$  →  $x_1=15$

$x_2=\frac{-5-35}{2}$  →   $x_2=-20$

We take the positive solution $x=15\ in$

Now we use equation (2) to find L

$L = x + 5$

$L = 15 + 5$

$L = 20\ in$