Geometric Fitting Problem: 3.5-Unit Triangle in 7-Unit Square

To solve this problem, we will find how many times a triangle can fit inside a square based on given dimensions:

• Step 1: Compute the area of the larger square.
• Step 2: Compute the area of the smaller square (side: $3.5$) which forms the base and height of the triangle.
• Step 3: Compute the area of the triangle using the area of the smaller square.
• Step 4: Divide the area of the larger square by the area of the triangle to find how many triangles fit.

Now, let's proceed with these calculations:
Step 1: Area of the large square = $7 \times 7 = 49$.
Step 2: Area of the smaller square = $3.5 \times 3.5 = 12.25$.
Step 3: Since the triangle fits perfectly within this square, and is a right isosceles triangle, its area = $\frac{1}{2} \times 3.5 \times 3.5 = 6.125$.
Step 4: Dividing the area of the large square by the area of the triangle: $\frac{49}{6.125} \approx 8$.

Therefore, the large square can completely fit exactly 8 triangles inside it.