The length of a rectangle can be represented by the expression x + 6. If the area of the rectangle is 2x ^ 2 + 8x - 24 , what is the expression for the width of the rectangle?
area = length * width
2x^2 + 8x - 24 = (x+6)(......)
you know the second bracket has to start with 2x, so ...
= (x + 6)(2x .....) , to get the -24 our second bracket must end with -4
= (x + 6)(2x - 4)
so the width is 2x-4
check by expanding my factors.
Well, the area of a rectangle is calculated by multiplying the length by the width. So, to find the width, we can use the formula:
Area = length x width
Given that the length is represented by the expression x + 6, and the area is 2x^2 + 8x - 24, we can substitute these values into the formula:
2x^2 + 8x - 24 = (x + 6) x width
Now, we can solve for the width. But before we do that, I just have to say... isn't it ironic that we're talking about the width of a rectangle while our own waistlines just keep expanding? Ah, the trials and tribulations of geometry and a love for pasta.
Okay, let's get back to business. Setting up the equation:
2x^2 + 8x - 24 = (x + 6) x width
Now, we can use our algebraic superpowers to solve for width. Get your capes ready, mathematical heroes!
*width appears*
Oh, look who decided to show up! It's the width!
So, after doing some calculations, the expression for the width of the rectangle is:
width = 2x - 4
There you have it! The width of the rectangle is 2x - 4. Keep this information in your mathematical toolkit, just in case you ever need to measure the dimensions of a rectangle or entertain a crowd with some geometry humor!
To find the expression for the width of the rectangle, we need to use the formula for the area of a rectangle, which is length multiplied by width.
Given:
Length of the rectangle = x + 6
Area of the rectangle = 2x^2 + 8x - 24
We can set up the equation:
Area of the rectangle = (Length) * (Width)
2x^2 + 8x - 24 = (x + 6) * (Width)
Now, let's solve this equation for the width.
First, let's expand the expression on the right side:
2x^2 + 8x - 24 = x * Width + 6 * Width
Now, let's combine like terms:
2x^2 + 8x - 24 = (x + 6) * Width
Next, we can divide both sides of the equation by (x + 6) to isolate the Width:
(2x^2 + 8x - 24) / (x + 6) = Width
Simplifying the equation further:
Width = 2x^2 + 8x - 24 / x + 6
Hence, the expression for the width of the rectangle is (2x^2 + 8x - 24) / (x + 6).
To find the expression for the width of the rectangle, we'll need to use the formula for the area of a rectangle, which is length multiplied by width.
Given that the length of the rectangle is represented by the expression x + 6, and the area of the rectangle is given by the expression 2x^2 + 8x - 24, we can set up the equation:
Area = Length * Width
Substituting the expressions, we have:
2x^2 + 8x - 24 = (x + 6) * Width
Now we can solve for the width by dividing both sides of the equation by the expression (x + 6):
Width = (2x^2 + 8x - 24) / (x + 6)
This gives us the expression for the width of the rectangle.