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 find out how many smaller triangles with side lengths of \( 5\sqrt{3} \) centimeters fit along the larger triangle with a side length of \( 40\sqrt{12} \) centimeters, we first simplify \( 40\sqrt{12} \).

Calculating \( \sqrt{12} \):
\[
\sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3}
\]

Now substituting back into the expression for the side length:
\[
40\sqrt{12} = 40 \cdot 2\sqrt{3} = 80\sqrt{3}
\]

Next, we need to find how many smaller triangles (with side length \( 5\sqrt{3} \) centimeters) fit into \( 80\sqrt{3} \) centimeters. This can be calculated by dividing the larger side length by the smaller side length:
\[
\text{Number of smaller triangles} = \frac{80\sqrt{3}}{5\sqrt{3}}
\]

When we divide, the \( \sqrt{3} \) cancels out:
\[
= \frac{80}{5} = 16
\]

Thus, the number of smaller right triangles that fit along the larger triangle's side length is

\[
\boxed{16}
\]