you can represent the width of a certain rectangle with the expression x + 2. the length of the rectangle is twice the width. what is the area of the rectangle?
A.) 2x+4
B.) 2x^2+8
C.) 2x^2+8x+8
D.) 4x^2+16x+16
I'm not sure on the answer..... Please help
Thank you
L = 2 x + 4
A = L w = (2x+4)(x+2)
= 2 x^2 + 8 x + 8 using foil
or use distributive property
2x(x+2) = 2 x^2 + 4 x
4 (x+2) = 4 x + 8
-------------------------add
2 x^2 + 8 x + 8 remarkable :)
Thank you Damon...remarkable is right!
Well, well, well, it seems like we have ourselves a rectangle mystery here! Let's get to the bottom of it, shall we?
First, we need to understand that the length of the rectangle is twice the width. So, if we represent the width with the expression (x + 2), then the length would be 2 times that, making it 2(x + 2).
Now, to find the area of the rectangle, we simply multiply the length by the width. So, the area (A) is given by:
A = width * length
A = (x + 2) * 2(x + 2)
To find the product, we have to apply the distributive property:
A = 2x(x + 2) + 2(2)(x + 2)
A = 2x^2 + 4x + 4x + 8
A = 2x^2 + 8x + 8
Ah, behold, the answer emerges like a clown from a tiny car! The area of the rectangle is C.) 2x^2 + 8x + 8.
So, my funny friend, I hope I've solved the riddle for you. You can now impress your buddies with your rectangle knowledge!
To find the area of a rectangle, we multiply its length by its width.
Given that the width is represented by the expression x + 2, and the length is twice the width, we can write the length as 2(x + 2) = 2x + 4.
Now, we can find the area by multiplying the width and length together:
Area = (x + 2)(2x + 4)
= 2x(x + 2) + 4(x + 2)
= 2x^2 + 4x + 4x + 8
= 2x^2 + 8x + 8
Therefore, the correct option for the area of the rectangle is C.) 2x^2 + 8x + 8.
To find the area of a rectangle, we need to multiply its length by its width.
In this case, the width is represented by the expression x + 2, and the length is twice the width.
So, the length of the rectangle would be 2 * (x + 2), which can be simplified to 2x + 4.
To find the area, we'll multiply the length and width:
Area = (2x + 4) * (x + 2)
To simplify this expression, we can use the distributive property:
Area = 2x * x + 2x * 2 + 4 * x + 4 * 2
Simplifying further:
Area = 2x^2 + 4x + 4x + 8
Combining like terms:
Area = 2x^2 + 8x + 8
So, the correct option for the area of the rectangle is C.) 2x^2 + 8x + 8.