The hypotenuse of a right triangle is centimetres and its area are square centimetres. Calculate the lengths of its perpendicular sides.

Question

The hypotenuse of a right triangle is  centimetres and its area are  square centimetres. Calculate the lengths of its perpendicular sides.

Philoid · Accepted Answer

Let the base be ‘x’ and perpendicular be ‘y’.

Area of triangle

⇒

⇒ 15 = xy … (1)

By Pythagoras Theorem,

(Base)² + (Height)² = (hypotenuse)²

⇒

⇒ … (2)

From equation (1),

⇒

⇒ 2(x² + 15) = 17 × x

⇒ 2x² + 30 = 17x

⇒ 2x² – 17x + 30 = 0

⇒ 2x² – 12x - 5x + 30 = 0

⇒ 2x (x – 6) – 5(x – 6) = 0

⇒ (2x – 5) (x – 6) = 0

2x – 5 = 0 or x – 6 = 0

2x = 5 or x = 6

or x = 6

Put in equation (2)

⇒

Put x = 6 in equation 2

⇒

∴ Base of triangle can be or 6

Perpendicular of triangle can be or 6.