Question

Huuuurrrryyy Pllllzzzzz!!!!?!???!!

Answer 1

By solving a quadratic equation, we will see that the width of the walkway is 3ft.

How to get the width of the walkway?

Remember that for a rectangle of length L and width W, the area is:

A = W*L

Now, we know that for our garden we have:

W = 8ft

L = 12ft

If we add a walkway of width x around the garden, then the new measures are:

W' = 8ft + 2x

L' = 12ft + 2x

So the area is:

A' = ( 8ft + 2x)*( 12ft + 2x)

And we know that it is equal to 192 ft^2, then:

192 ft^2 = ( 8ft + 2x)*( 12ft + 2x)

Now we can solve this for x.

192ft^2 = 96ft^2 + 4x^2 + 20ft*x

0 = 96ft^2 - 192ft^2 + 20ft*x + 4x^2

0 = -96ft^2 + 20ft*x + 4x^2

This is a quadratic equation, and the solutions are given by the Bhaskara's formula:

$x = \frac{-20ft \pm \sqrt{(20ft)^2 - 4*4*(-96ft^2)} }{2*4} \\\\x = \frac{-20ft \pm 44ft}{8}$

We only take the positive solution, so we get:

x = (-20ft + 44ft)/8 = 3ft

So the width of the walkway is 3ft.

If you want to learn more about quadratic equations, you can read:

brainly.com/question/1214333