SOLUTION: A 30 inch by 40 inch countertop for a work island is to be covered with green ceramic tiles, except for a border of uniform width, if the area covered by green tiles is 704 square

Question 149810: A 30 inch by 40 inch countertop for a work island is to be covered with green ceramic tiles, except for a border of uniform width, if the area covered by green tiles is 704 square inches (in^2 ) , then how wide is the border?
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=width of border.

First, let's draw the picture.

note: the lengths and are due to the subtraction of 2 "x" lengths. Take note that there are two dashed lines per side that are not part of the green tiles.

From the picture, we see that the actual counter top is by . So the length is and the width is

Now remember, the area of a rectangle is

Plug in the given area of the green tiles , and

FOIL

Subtract 704 from both sides.

Combine like terms.

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, we need to see if they generate reasonable lengths and widths

Let's check the solution

Go back to the length equation

Plug in

Multiply

Subtract

Since a negative length is not possible, this means that the value is a reasonable solution.

----------------------------

Let's check the solution

Go back to the length equation

Plug in

Multiply

Subtract

So we get a reasonable length with

--------

Go back to the width equation

Plug in

Multiply

Subtract

So we also get a reasonable width with

===============================================

Answer:

So the only solution is

So the width of the border is 4 inches
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let the width of the border =

Use quadratic formula to solve

this is too large to use
in answer
check answer:

OK
RELATED QUESTIONS
ryan is using tiles in his bathroom. He chooses 1-inch by 2-inch tiles for the border and (answered by richwmiller)
Cheryl is redoing her bathroom and has selected ceramic tiles for the 5 foot by 8 foot... (answered by greenestamps)
A floor 8m 20cm by 6m is to be covered with a tiles of size 20cm by15cm. Find the number... (answered by Alan3354)
Jessica is decorating a section of one wall of her kitchen with ceramic tiles. The area... (answered by checkley77)
Sarah is renovating her kitchen and has decided to use tiles on her countertop which is... (answered by jorel1380)
Hi, I need help on my summer assignment, i did all of them except two...which i don't... (answered by RAY100,stanbon)
A bathroom floor measures 12 feet 8 inches wide by 18feet 9 inches long. This floor is... (answered by unlockmath)
A caf� owner is designing a new menu and wants to include a decorative border around the... (answered by josgarithmetic)
A 4-inch by 6-inch picture is enlarged for framing by tripling its dimensions. A... (answered by mananth)