Question

given the following side lengths of a triangle, use the pythagorean theorem to determine whether the triangle is a right triangle.
a = 3 cm
b = 4 cm
c = 5 cm
show your work here
hint: to add the square root symbol ($\sqrt{\square}$), type root
true false

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem states that for a right triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side) and \(a\), \(b\) are the other two sides. Here, \(c = 5\) cm (the longest side), \(a=3\) cm and \(b = 4\) cm.

Step2: Calculate \(a^{2}+b^{2}\)

Calculate \(a^{2}\) and \(b^{2}\): \(a^{2}=3^{2}=9\), \(b^{2}=4^{2} = 16\). Then \(a^{2}+b^{2}=9 + 16=25\).

Step3: Calculate \(c^{2}\)

Calculate \(c^{2}\): \(c^{2}=5^{2}=25\).

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(a^{2}+b^{2}=25\) and \(c^{2}=25\), we have \(a^{2}+b^{2}=c^{2}\). So the triangle is a right triangle.

Answer:

True