Question

isabella has sticks that are 10cm, 11cm, and 13cm long. can she place the sticks together to form a right triangle? justify your answer.

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the length of the hypotenuse (the longest side) and \(a\) and \(b\) are the lengths of the other two sides.
Here, \(a = 10\), \(b=11\), \(c = 13\)
Calculate \(a^{2}=10^{2}=100\), \(b^{2}=11^{2}=121\), \(c^{2}=13^{2}=169\)

Step2: Check the Pythagorean theorem condition

Check if \(a^{2}+b^{2}=c^{2}\)
\(a^{2}+b^{2}=100 + 121=221
eq169=c^{2}\)

Answer:

No, because \(100 + 121\) does not equal \(169\)