Which equation could be used to find the dimensions of a room that has a length of 8 feet longer than the width, x, and has an area of 240 square feet?
(A) x squared - 8x + 240 = 0
(B) 2x(2x-8x+16)=240
(C) x squared + 8x + 240 = 0
(D) x squared + 8x - 240 = 0
I got (x)(8x)=240 aka x squared + 8x = 240, which isn't any of the answer choices. I'm leaning towards (B) though, but I don't understand. Can someone please help me figure this one out? Thanks.
Responses
* Algebra - bobpursley, Sunday, May 4, 2008 at 5:45pm
You should have started with Length times width.... (8+x)x=240
o Algebra - Anonymous, Sunday, May 4, 2008 at 8:07pm
I know. That was a typo. So where do I go from there?
To find the dimensions of the room, you need to solve the equation (8+x)(x)=240. This equation represents the length of the room (8+x) multiplied by the width of the room (x) equaling the area of the room (240 square feet).
To solve this equation, you can start by expanding the product on the left side: 8x + x^2 = 240.
Next, you want to bring all the terms to one side of the equation to set it equal to zero. So, rearrange the equation to be: x^2 + 8x - 240 = 0.
Now you can see that the correct answer choice is (D) x^2 + 8x - 240 = 0.
To solve this quadratic equation, you can factor it, complete the square or use the quadratic formula. In this case, factoring is the most efficient method.
To factor the equation, you need to find two numbers that multiply to -240 and add up to 8. After some trial and error, you find that 20 and -12 satisfy these conditions. So, you can factor the equation as (x + 20)(x - 12) = 0.
Now you have two equations: x + 20 = 0 and x - 12 = 0. Solving these equations gives you x = -20 and x = 12. Since the width cannot be negative, the only valid solution is x = 12.
Therefore, the width of the room is 12 feet. To find the length, you can substitute this value back into the original equation: length = 8 + x = 8 + 12 = 20 feet.
So, the dimensions of the room are 12 feet (width) and 20 feet (length).
To find the equation for the dimensions of the room, you need to start with the formula for the area of a rectangle: Length times width. In this case, the length is given as 8 feet longer than the width, so you can express the length as x + 8. The width is simply x.
So, the equation for the area of the room becomes: (x + 8) * x = 240.
Now, let's look at the answer choices:
(A) x squared - 8x + 240 = 0: This is not the correct equation because it does not match the equation we derived.
(B) 2x(2x-8x+16)=240: This is not the correct equation either, as it is not equivalent to our equation.
(C) x squared + 8x + 240 = 0: This is also not the correct equation, as it does not match our derived equation.
(D) x squared + 8x - 240 = 0: This is the correct equation! It is equivalent to our derived equation (x + 8) * x = 240.
Therefore, the correct equation to find the dimensions of the room is (D) x squared + 8x - 240 = 0.