Isabella has sticks that are 10cm, 11cm, and 13cm long. Can she place the sticks together to form a right triangle? Justify your answer.(1 point)

Responses

No, because 10+11 does not equal 13
No, because 10+11 does not equal 13

Yes, because there is a small side, medium side and long side
Yes, because there is a small side, medium side and long side

No, because 100+121 does not equal 169
No, because 100+121 does not equal 169

Yes, because a triangle has 3 sides

1 answer

To determine if the sticks can form a right triangle, we can use the Pythagorean theorem. For three lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), a right triangle can be formed if the following condition holds:

\[ a^2 + b^2 = c^2 \]

Given the stick lengths are 10 cm, 11 cm, and 13 cm, we identify the longest stick (13 cm) as \(c\), and the other two sticks (10 cm and 11 cm) as \(a\) and \(b\).

Now, we calculate:

  • \(a^2 = 10^2 = 100\)
  • \(b^2 = 11^2 = 121\)
  • \(c^2 = 13^2 = 169\)

Now, we check if \(a^2 + b^2 = c^2\):

\[ 100 + 121 = 221 \] \[ c^2 = 169 \]

Since \(221 \neq 169\), the condition does not hold. Therefore, they cannot form a right triangle.

The correct response is: No, because 100+121 does not equal 169.