Question

given the following side lengths of a triangle, use the pythagorean theorem to determine whether the triangle is a right triangle.
a = 33 yd
b = 56 yd
c = 65 yd
show your work here
hint: to add the square root symbol (√□), type
oot\
true false

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\) where \(c\) is the hypotenuse (longest side). Here, \(a = 33\), \(b = 56\), \(c = 65\). Calculate \(a^2\): \(33^2 = 1089\).

Step2: Calculate \(b^2\)

\(56^2 = 3136\).

Step3: Sum \(a^2\) and \(b^2\)

\(1089 + 3136 = 4225\).

Step4: Calculate \(c^2\)

\(65^2 = 4225\).

Step5: Compare sums

Since \(a^2 + b^2 = 4225\) and \(c^2 = 4225\), they are equal.

Answer:

True