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 t…

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asked Jun 1, 2020 176k views

2 Answers

Shnigi · Answer 1 · 2020-06-05T16:17:37+0000

Answer:

Width = 15 inches Length = 20 inches

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:

$x=(-b\±√(b^2-4ac))/(2a)$

In this case note that:

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

Then:

$x=(-5\±√((5)^2-4(1)(-300)))/(2(1))$

$x=(-5\±√(25+1200))/(2)$

$x=(-5\±√(1225))/(2)$

$x=(-5\±35)/(2)$

x_1=(-5+35)/(2) →
x_1=15

x_2=(-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

$L = 20\ in$