Question

Mike is building a bridge for a contest and wants to make a right triangle out of

three popsicle sticks that measure 6 cm, 9 cm, and 15 cm. Can he make a right
triangle out of these lengths?

Answer 1

Mike cannot make a right triangle out of popsicle sticks measuring 6 cm, 9 cm, and 15 cm.

Step-by-step explanation:

To determine if Mike can make a right triangle out of the popsicle sticks, we need to check if the sum of the squares of the two shorter sides is equal to the square of the longest side. Let's calculate:

Short side 1: 6 cm

Short side 2: 9 cm

Hypotenuse: 15 cm

Now, let's compute:

Short side 1 squared: 6 cm x 6 cm = 36 cm^2

Short side 2 squared: 9 cm x 9 cm = 81 cm^2

Hypotenuse squared: 15 cm x 15 cm = 225 cm^2

Finally, let's add the squares of the two shorter sides:

36 cm^2 + 81 cm^2 = 117 cm^2

Based on our calculations, the sum of the squares of the two shorter sides is 117 cm^2. However, the square of the longest side (225 cm^2) is greater than this sum. Therefore, Mike cannot make a right triangle with popsicle sticks of lengths 6 cm, 9 cm, and 15 cm.