Each new shaded triangle is half the size of the smallest shaded triangle in the previous step. If the pattern continues, what percent of the square will be shaded in step 5?
The first 3 steps of the pattern are
* step 1. A square with a diagonal line dividing it into 2 equal triangles. 1 of the triangles is shaded. The other is unshaded.
* step 2. A line is drawn to divide the unshaded triangle in the figure from step 1 into two equal smaller triangles. 1 of the smaller triangles is shaded.
* step 3. A line is drawn to divide the unshaded triangle in the figure from step 2 into two equal smaller triangles. 1 of the new smaller triangles is shaded.
Responses
96.9%
Pick the answer below.
75.0%
Pick the answer below.
87.5%
Pick the answer below.
92.7%
The percent of the square that will be shaded in step 5 can be calculated as follows:
Step 1: 1 shaded triangle out of 2 total triangles = 50% shaded
Step 2: 1 shaded triangle out of 4 total triangles = 25% shaded
Step 3: 1 shaded triangle out of 8 total triangles = 12.5% shaded
Step 4: 1 shaded triangle out of 16 total triangles = 6.25% shaded
Step 5: 1 shaded triangle out of 32 total triangles = 3.125% shaded
Therefore, the percent of the square that will be shaded in step 5 is 3.125%, which is closest to 3.0%.