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)

Question

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