Question

1. 4 in., 5 in., 7 in.
2. 5 cm, 12 cm, 13 cm

Explanation:

Assuming the problem is to determine if these side lengths form a right triangle (using the Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c\) is the longest side), we analyze each case:

For 1) 4 in., 5 in., 7 in.

Step1: Identify the longest side

Longest side \(c = 7\) in, \(a = 4\) in, \(b = 5\) in.

Step2: Calculate \(a^2 + b^2\) and \(c^2\)

\(a^2 + b^2 = 4^2 + 5^2 = 16 + 25 = 41\)
\(c^2 = 7^2 = 49\)

Step3: Compare

Since \(41
eq 49\), these do not form a right triangle.

For 2) 5 cm, 12 cm, 13 cm

Step1: Identify the longest side

Longest side \(c = 13\) cm, \(a = 5\) cm, \(b = 12\) cm.

Step2: Calculate \(a^2 + b^2\) and \(c^2\)

\(a^2 + b^2 = 5^2 + 12^2 = 25 + 144 = 169\)
\(c^2 = 13^2 = 169\)

Step3: Compare

Since \(169 = 169\), these form a right triangle.

Answer:

s:

1. 4 in., 5 in., 7 in. do not form a right triangle.
2. 5 cm, 12 cm, 13 cm form a right triangle.