Question

The area right angle triangle 30sqcm,hypotneus 13cm.find length smaller side?

Answer 1

let base be b and height be h,
Area => 1/2 × b × h = 30
=> b×h = 60
According to Pythagoras theorem ,
b² + h² = 13² = 169
Now,
(b+h)² = b² + h² + 2bh = 169 + 2×60 = 389
=> b + h = √389 = 17 --------- (eq.1)
Now,
(b-h)² = b²+h²-2bh = 169 - 120 = 49
=> b - h = √49 = 7 ---------- (eq.2)
From eq.1 and eq.2
base = 12cm
height = 5cm