To answer, allow the width of the frame to be represented by x. The dimensions of the frame should then be, 11+2x and 6+2x. Subtracting the area of the inside of the frame from the area of the outside should be able to give us 18 cm². The equation,
(11 + 2x)(6 + 2x) - (11)(6) = 18
The value of x from the equation is equal to 0.5. Thus, the width of the frame should be 0.5 cm.
P = 2(L + W)
P = 150
L = 5W + 7
150 = 2(5W + 7 + W)
150 = 2(6W + 7)
150 = 12W + 14
150 - 14 = 12W
136 = 12W
136/12 = W
11.33 (or 11 1/3) = W <=== width
L = 5W + 7
L = 5(34/3) + 7
L = 170/3 + 7
L = 170/3 + 21/3
L = 191/3 (or 63 2/3) = L <=== length
% increase = Increase ÷ Original Number × 100. If the answer is a negative number, that means the percentage change is a decrease.
This is just some pythagorean theorem, or a^2 + b^2 = c^2. We have a and b, which is 9 and 12, and we need to find c. To find c, we need to first square those, giving u 81 and 144. Now, we need to add them, giving us 225, meaning c^2 = 225. However, we need to find c on its own, so we have to find the square root of 225. That would be 15.
We know that the side lengths of the square base are: x * x. The volume is 12, so for now, let's say that y is the other side length. Then, x * x * y = 12. We can solve for y: y = 12/x^2. Now, we find the surface area of the 5 sides.
Four of the sides have the same area: x * (12/x^2) = 12/x, so we multiply this by 4: 48/x.
The last side is the base: x * x = x^2.
We add 48/x to x^2:
x^2 + 48/x
So, the answer is the fourth choice, (d).
