The difference between the two perpendicular sides of a right-angled triangle is 17 cm and its area is 84 cm². What is the perimeter (in cm) of the triangle?

Solution (By Examveda Team)

P - B = 17 (Given)
Area = $$\frac{1}{2}$$ × B × P
BP = 2 × 84
BP = 168 . . . . . . (i)
P - B = 17
Squaring both side
P² + B² - 2BP = 289
H² - 2(168) = 289 (∴ H² = P² + B²)
H² = 289 + 336
H = $$\sqrt {625} $$
H = 25 cm
(P + B)² = P2 + B2 + 2PB
(P + B)² = 625 + 2(168)
(P + B)² = 625 + 336
P + B = $$\sqrt {961} $$
P + B = 31
∴ H + P + B = 31 + 25 = 56