Question

1. 51 m, 68 m, 85 m

Explanation:

Assuming the problem is to check if these lengths form a right triangle (using the Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c\) is the longest side).

Step1: Identify sides

Let \(a = 51\), \(b = 68\), \(c = 85\) (since 85 is the longest).

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

\(a^2 = 51^2 = 2601\), \(b^2 = 68^2 = 4624\)
\(a^2 + b^2 = 2601 + 4624 = 7225\)

Step3: Calculate \(c^2\)

\(c^2 = 85^2 = 7225\)

Step4: Compare

Since \(a^2 + b^2 = c^2\) (\(7225 = 7225\)), the triangle is right - angled.

Answer:

The lengths 51 m, 68 m, 85 m form a right - angled triangle (by the Pythagorean theorem).