Question

directions the lengths of the sides of various triangles are given below. is the triangle a right triangle? 1) 4 in., 5 in., 7 in.

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 longest side, and \(a\), \(b\) are the shorter sides.

Step2: Identify sides and calculate squares

Here, the sides are 4 in, 5 in, 7 in. The longest side \(c = 7\), \(a = 4\), \(b = 5\).
Calculate \(a^2 = 4^2 = 16\), \(b^2 = 5^2 = 25\), \(c^2 = 7^2 = 49\).

Step3: Check Pythagorean theorem

Sum of \(a^2\) and \(b^2\) is \(16 + 25 = 41\). Compare with \(c^2 = 49\). Since \(41
eq49\), the Pythagorean theorem does not hold.

Answer:

No (the triangle with sides 4 in, 5 in, 7 in is not a right triangle)