Answer:
66 (C)
Step-by-step explanation:
For the starting figure, you know that each block has a width of 10, and a height of 5 cm. If you are calculating the perimeter, then the only parts of the figure that matter are the outsides.
When we add a layer, we replace the perimeter along the bottom (with an equal length, so the perimeter is not changing along the base).
But we also add the length of added rectangles to the sides, and that is not replacing the perimeter already on the previous layer--it is increasing the perimeter by 10 cm (5 cm on both sides).
So, if we want to find the perimeter of figure 1, we can calculate the top (10 cm + 10 cm on top, 5 cm + 5 cm for the sides of the block on top, 5cm + 5 cm for the outsides of the lower layer, 10cm + 10cm for the bottom base) (60cm is the perimeter).
Each layer we add it adding 10cm. So, the perimeter of figure 2 is 60 + 10, or 70cm.
To find how many layers we have added to the figure n, we should first subtract the original 60 cm, so that we can find how much we have added. 710 - 60 = 650.
So, we have added 650 cm to the perimeter of our figure. We know that we are adding 10 cm at a time, so to find how many times we have had to add a layer, we need to divide 650 / 10 , to get 65. We have added a layer 65 times.
The first layer is +0 times, the second is +1, the third is +2, so the +65 is going to be the 66th layer, making the answer 66.
