Question

a right Triangle has a a hyper tennis of length PCM and one side of the length 2 centimetre if if P minus Q is equals to 1 find the length of the third side of the triangle​

Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

A right triangle has a hypotenuse of length p cm & one side of length q cm. If p - q = 1.

$\underline{\bf{Explanation\::}}$

Firstly, attachment a figure of right angled Δ a/c to the given question.

We have,

→ p - q = 1..............(1)

Let the third side of a triangle be r

$\underline{\underline{\tt{By\:using\:Pythagoras\:theorem\::}}}$

⇒ (Hypotenuse)² = (Base)² + (Perpendicular)²

⇒ (p)² = (q)² + (r)²

⇒ (r)² = (p)² - (q)²

⇒ (r)² = (p+q) (p-q)   [ ∴formula a² - b² ]

⇒ (r)² = (p+q) × (1)     [∴from (1)]

⇒ (r)² = p + q

⇒ r = √p + q

Thus,

The third side of the triangle will be √p + q cm .