A square painting is surrounded by a frame. the outside edges of the frame are x inches in length, and the frame is 3 inches thick. What is the total area of the frame?
A)-12x+36
B)12x-36
C)x^2+12x+36
D)x^2-12x-36
Is it C or D?
the 3" frame is on both sides, so you need
x^2 - (x-6)^2 = 12x-36
The answer if there is a 2-inch border would be 8x-16
Step by Step:
2(2x) + 2(2)(x - 4)
Multiply 2 times 2x and 2 times 2:
4x + 4 (x - 4)
Use Distributive Property to multiply 4 times x and 4 times - 4 (negative 4):
4x + 4x - 16
Then add like terms, 4x plus 4x:
8x - 16
Here is what I get:
x^2 - (x-3)^2 =
x^2 - (x^2 - 6x + 9) =
x^2 - x^2 + 6x - 9) = 6x - 9
Typos?
A square painting is surrounded by a frame. The outside edges of the frame are x inches in length and there is a 2-inch border between the painting and the frame. What is the total area of the border?
Well, painting frames can be quite picky! They always demand to be the center of attention. So, let's give this square painting the attention it deserves!
Now, to calculate the total area of the frame, we need to figure out the area of the outer square minus the area of the inner square.
The outer square has sides of length x + 6 (since the frame is 3 inches thick on all sides). Therefore, its area is (x + 6)^2.
The inner square has sides of length x (since it's the painting itself). Therefore, its area is x^2.
Now, to find the total area of the frame, we subtract the area of the inner square from the area of the outer square:
Total area of frame = (x + 6)^2 - x^2
Expanding this equation, we get:
Total area of frame = x^2 + 12x + 36 - x^2
Simplifying further:
Total area of frame = 12x + 36
So, the correct answer is option A) 12x + 36.
Happy framing!
To find the total area of the frame, we need to subtract the area of the inner square from the area of the outer square.
The outer square will have a side length of the sum of the frame thickness (3 inches) and the side length of the inner square (which is x inches). So the side length of the outer square will be (x + 3) inches.
The area of the outer square is then (x + 3)^2 square inches.
The inner square, on the other hand, will have a side length of just x inches. So the area of the inner square is x^2 square inches.
Now, to find the area of the frame, we subtract the area of the inner square from the area of the outer square:
Total Area of Frame = Area of Outer Square - Area of Inner Square
= (x + 3)^2 - x^2
= x^2 + 6x + 9 - x^2
= 6x + 9
Now, let's compare this expression with the options given:
C) x^2 + 12x + 36
The expression in option C has additional terms (12x + 36) compared to our result (6x + 9). Therefore, option C is not correct.
D) x^2 - 12x - 36
The expression in option D has different signs (-) for both terms. Our result has positive terms. Therefore, option D is not correct.
Since our result is 6x + 9, none of the given options match the correct answer.