A right triangle has hypotenuse of length q cm and one side of length p cm if q-p =2 cm, - Maths - Heron\s Formula

Question

A right triangle has hypotenuse of length q cm and one side of
length p cm if q-p =2 cm, find the lengh of third side of triangle
in terms of q

Priyanka Kedia · Accepted Answer

$L e t A B C b e a r i g h t t r i a n g l e r i g h t a n g l e d a t C . S o, h y p o t e n u s e (A B) = q c m L e t o n e s i d e o f l e n g t h (A C) = p c m G i v e n, q - p = 2 \Rightarrow p = q - 2 ..... (1) U \sin g P y t h a g o r a s t h e o r e m i n Δ A B C, {A B}^{2} = {A C}^{2} + {B C}^{2} \Rightarrow q^{2} = p^{2} + {B C}^{2} \Rightarrow {B C}^{2} = q^{2} - p^{2} ..... (2) S u b s t i t u t e v a l u e o f p f r o m e q u a t i o n (2) i n e q u a t i o n (1), w e g e t, {B C}^{2} = q^{2} - {(q - 2)}^{2} \Rightarrow {B C}^{2} = q^{2} - (q^{2} + 4 - 4 q) \Rightarrow {B C}^{2} = q^{2} - q^{2} - 4 + 4 q \Rightarrow {B C}^{2} = 4 (q - 1) \Rightarrow B C = 2 \sqrt{q - 1} c m H e n c e l e n g t h o f t h i r d s i d e o f t r i a n g l e i s 2 \sqrt{q - 1} c m .$

A right triangle has hypotenuse of length q cm and one side of length p cm if q-p =2 cm, find the lengh of third side of triangle in terms of q