Question

Maura is creating a quilt using right triangles. A large right triangle with a side length of 40√12
centimeters has smaller right triangles with side lengths of 5√3
centimeters along it. How many smaller lengths are running along the longer length?(1 point)

Answer 1

To determine how many smaller right triangles with side lengths of \(5\sqrt{3}\) centimeters fit along the longer side of the large right triangle with side length \(40\sqrt{12}\) centimeters, we need to first identify the longer side of the larger triangle and then divide it by the length of the smaller triangles.

1. **Calculate the long side of the large triangle:**
- The side length of the large triangle is given as \(40\sqrt{12}\) centimeters.
- We can simplify this:
\[
\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}
\]
Thus,
\[
40\sqrt{12} = 40 \times 2\sqrt{3} = 80\sqrt{3}
\]

2. **Determine how many smaller triangles fit along this length:**
- Each smaller triangle has a side length of \(5\sqrt{3}\).
- We need to divide the length of the large triangle by the length of a smaller triangle:
\[
\text{Number of smaller triangles} = \frac{80\sqrt{3}}{5\sqrt{3}}
\]
3. **Simplify the division:**
- The \(\sqrt{3}\) terms cancel out:
\[
\frac{80\sqrt{3}}{5\sqrt{3}} = \frac{80}{5} = 16
\]

Therefore, **the number of smaller triangles that can fit along the longer side of the larger triangle is** \(\boxed{16}\).