Area of a right triangle is 240 cm². If its one side other than the hypotenuse…

Concept: For a right triangle with legs a and b and hypotenuse c, the area is ½ × a × b, and the Pythagorean theorem gives c2 = a2 + b2. The perimeter is the sum of all three sides: a + b + c.

1. Let the two legs be a = 30 cm and b (unknown), with hypotenuse c. From the area formula: ½ × 30 × b = 240.

2. Solving for b: 15 × b = 240, so b = 16 cm.

3. Apply the Pythagorean theorem for the hypotenuse: c2 = 302 + 162 = 900 + 256 = 1156, so c = √1156 = 34 cm.

4. Perimeter = a + b + c = 30 + 16 + 34 = 80 cm.

Cross-check: 30, 16, and 34 form a scaled Pythagorean triple — twice 15, 8, and 17 — and 152 + 82 = 225 + 64 = 289 = 172, confirming the hypotenuse of 34 cm and hence the perimeter of 80 cm.