Maths- AS

Let the three sides be (a - d) cm, a cm and (a + d) cm.

(a - d) + a + (a + d) = 60
3a = 60
a = 20

It is a right-angled triangle, so
(a - d)² + a² = (a + d)²
(20 - d)² + 20² = (20 + d)²
400 - 40d + d² + 400 = 400 + 40d + d²
- 40d + 400 = 40d
80d = 400
d = 5

The three sides of the right-angled triangle are 15 cm, 20 cm, 25 cm.

The area of the triangle is (15 × 20) ÷ 2 = 150 cm².

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