james has a metal frame with an 8.32 inch perimeter. If the sides are 0.04 inches thick, what is the perimeter of the inside of the frame?
0.04 x 4 + .16
8.32 - .16 = 8.16
But the book gives an answer of 8.
I am not sure what I am doing wrong. Can any one help me out. The book doesn't explain the answer.
The assumption to be made is that the frame is a square or a rectangle thought the question doesn't specify it.
In this explanation a square frame is used though a rectangular frame will also work.
Draw a large square.
Now draw a smaller square in the larger square.
Mark the sides of the larger square X.
Now maker the sides of the smaller square Y.
Now mark the distance between adjacent sides of the large and small square as 0.04 (thickness of frame).
Now you should notice that length of any side of the smaller square is X-0.04-0.04 = X - 0.08.
Therefore the perimeter of the smaller square is (X - 0.08) + (X - 0.08) + (X - 0.08) + (X - 0.08) = 4X - 0.32
We know that 4X (sum of each side of larger square) is 8.32
Therefore
4X - 0.32 = perimeter of small square
8.32 - 0.32 = 8
What shape is this frame?
If it's a rectangle, then I think your answer is correct.
It only says a metal frame. Thank you so much for helping me with this so quickly. :)
Drawing this helps a whole lot.
To find the perimeter of the inside of the frame, you can subtract the total thickness of the sides from the perimeter of the metal frame.
The metal frame has a perimeter of 8.32 inches. Since the frame has four sides and each side is 0.04 inches thick, the total thickness of all four sides would be 0.04 inches multiplied by 4, which equals 0.16 inches.
Therefore, the perimeter of the inside of the frame would be the perimeter of the metal frame (8.32 inches) minus the total thickness of the sides (0.16 inches). Subtracting 0.16 inches from 8.32 inches gives you 8.16 inches.
Based on your calculations, it seems that you have correctly determined the perimeter of the inside of the frame to be 8.16 inches. It is possible that there might be a mistake in the book or an error in the answer provided. Double-checking your calculations and considering the given information should give you the correct result.