Question

Charlie draws a large right triangle. Using identical square tiles, he uses 25 tiles to create a square along one leg of the triangle and 144 tiles to create a square along the other leg of the triangle. How many of the same square tiles will he need to create a square along the hypotenuse of the triangle?(1 point)
Responses

169
169

25
25

119
119

144

Answer 1

To determine the number of square tiles needed to create a square along the hypotenuse of the triangle, we first need to find the lengths of the legs of the triangle based on the number of tiles used.

1. **Calculate the side lengths:**
- For one leg, using 25 tiles, the length of this leg (let's call it \( a \)) is:
\[
a = \sqrt{25} = 5
\]
- For the other leg, using 144 tiles, the length of this leg (let's call it \( b \)) is:
\[
b = \sqrt{144} = 12
\]

2. **Use the Pythagorean theorem to find the hypotenuse:**
The hypotenuse (\( c \)) can be found using the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2} = \sqrt{5^2 + 12^2}
\]
Calculating \( 5^2 \) and \( 12^2 \):
\[
5^2 = 25, \quad 12^2 = 144
\]
Now, add these:
\[
a^2 + b^2 = 25 + 144 = 169
\]
Therefore, the length of the hypotenuse is:
\[
c = \sqrt{169} = 13
\]

3. **Determine the number of tiles needed for the hypotenuse:**
The number of square tiles needed to create a square along the hypotenuse (side length of \( c \)) is:
\[
\text{Number of tiles} = c^2 = 13^2 = 169
\]

Thus, Charlie will need **169 tiles** to create a square along the hypotenuse. The correct response is:

**169**