The sides of a triangular field are 360 m, 480 m and 600 m. Its area is equal to the area of a square field. What is the side (in m) of the square field?

$120 \sqrt{6}$

We know that,

Area of triangle = \(\frac{1}{2}\) × Base × Height

Area of square = Side²

We have,

The sides of a triangular field = 360 m, 480 m and 600 m.

We know that, this is a right angled triangle.

It means height = 480 and base = 360, and 600 = Hypotenuse

Area of triangle = \(\frac{1}{2}\)  (360 × 480) = 86400 cm²

According to the question,

Its area is equal to the area of a square field.

= side² = 86400

= side = 120\(\sqrt {6}\) cm