Question

1. dawn would like to join three straws that measure 4.5 inches, 6 inches and 7.5 inches together to form a triangle. will the triangle be a right triangle? explain.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the sum of the squares of the two shorter sides (legs) should equal the square of the longest side (hypotenuse). The formula is \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs.

Step2: Identify sides

The lengths are \(4.5\) in, \(6\) in, and \(7.5\) in. The longest side is \(7.5\) in, so let \(a = 4.5\), \(b = 6\), \(c = 7.5\).

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

\(a^2=(4.5)^2 = 20.25\), \(b^2=(6)^2 = 36\). Then \(a^2 + b^2=20.25 + 36 = 56.25\).

Step4: Calculate \(c^2\)

\(c^2=(7.5)^2 = 56.25\).

Step5: Compare

Since \(a^2 + b^2 = c^2\) (both equal \(56.25\)), by the Pythagorean theorem, the triangle is a right triangle.

Answer:

Yes, the triangle will be a right triangle. Because when we check the Pythagorean theorem (\(a^2 + b^2 = c^2\)) with \(a = 4.5\), \(b = 6\), and \(c = 7.5\), we find that \(4.5^2+6^2 = 20.25 + 36 = 56.25\) and \(7.5^2 = 56.25\), so \(4.5^2+6^2 = 7.5^2\), satisfying the condition for a right triangle.