Question

1. does a triangle with sides of lengths 1.5 ft, 2.5 ft, and 2 ft form a right triangle? how do you know?

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.

Step2: Identify the sides

Let \(a = 1.5\) ft, \(b = 2\) ft, and \(c = 2.5\) ft.

Step3: Calculate \(a^{2}+b^{2}\)

\(a^{2}+b^{2}=(1.5)^{2}+2^{2}=2.25 + 4=6.25\)

Step4: Calculate \(c^{2}\)

\(c^{2}=(2.5)^{2}=6.25\)

Step5: Compare

Since \(a^{2}+b^{2}=c^{2}\), the triangle is a right - triangle.

Answer:

Yes, because \(1.5^{2}+2^{2}=2.25 + 4 = 6.25\) and \(2.5^{2}=6.25\), satisfying the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\).