If the perimeter of a right-angled triangle is 56 cm and

Home » Aptitude » Mensuration » Question

If the perimeter of a right-angled triangle is 56 cm and area of the triangle is 84 sq. cm, then the length of the hypotenuse is (in cm)

a + b + c = 56 ...(i)

	1	ac = 84
	2

⇒ ac = 168 sq.cm.
∴ b² = a² + c²
⇒ b² = (a + c)² – 2ac
⇒ b² = (56 – b)² – 2 × 168 [By (i)]
⇒ b² = 3136 – 112 b + b² – 336
⇒ 112b = 2800

⇒ b =	2800	= 25cm
	112