Question

1. if rs = 35, st = 37, and rt = 71, is △rst a right triangle? explain. enter your answer.

Explanation:

Step1: Recall Pythagorean theorem

For a triangle to be a right triangle, the sum of the squares of the two shorter sides should equal the square of the longest side. Let's identify the sides: \( RS = 35 \), \( ST = 37 \), \( RT = 71 \). The two shorter sides are \( 35 \) and \( 37 \), the longest is \( 71 \).

Step2: Calculate squares of sides

Calculate \( 35^2 = 1225 \), \( 37^2 = 1369 \), and \( 71^2 = 5041 \).

Step3: Sum of squares of shorter sides

Sum the squares of the two shorter sides: \( 1225 + 1369 = 2594 \).

Step4: Compare with square of longest side

Now, compare \( 2594 \) with \( 5041 \). Since \( 2594
eq 5041 \), the Pythagorean theorem does not hold.

Answer:

No, \(\triangle RST\) is not a right triangle because \(35^2 + 37^2 = 2594\) and \(71^2 = 5041\), and \(2594
eq5041\), so the Pythagorean theorem does not hold.