Question

the hypotenuse of a right angled triangle is 6 cm more than twice the shorter side if the third side is 2cm less than the hypotenuse find the lenghts of 3 sides​

Answer 1

Answer:

Length of Hypotenuse = 26 cm

Step-by-step explanation:

Let the shortest side be x cm

The hypotenuse of a right angled triangle is 6 cm more than twice of the shortest side

⇒ Hypotenuse = 2x + 6

The third side is 2 cm less than the hypotenuse

⇒ Third side = 2x - 4

Now, applying Pythagoras theorem

Hypotenuse² = (Shorter side)² + (Third side)²

⇒ (2x + 6)² = x² + (2x + 4)²

⇒ 4x² + 36 + 24x = x² + 4x² + 16 + 16x

⇒ x² - 8x - 20 = 0

⇒ (x + 2)(x - 10) = 0

⇒ x = -2 or x = 10

Since, The length of the side cannot be negative. so x = -2 is rejected

Hence, x = 10

⇒ Length of Hypotenuse = 2x + 6 = 2 × 10 + 6 = 26 cm

Answer 2

side of hypotenuse is 6cm more than twice the shorter side

let the shorter side be x

therefore

hypotenuse = 2x+6 cm

third side = 2x+6-3

=2x+3