Question

the hypotenuse of right angle triangle is 25cm the difference between length of the other two side of triangle is 5 find the length of these two sides​

Answer 1

${\huge{\red{\underline{\underline{Answes}}}}}$

$\mathrm\pink{\:Let's \:take \:first \:side \:angle \:as = x}$

$\mathrm\pink{\:And \:second \:angle \:as = x + 5}$

$\huge\bf\boxed{\boxed{\underline{\red{\:By \:Pythagoras \:theorem}}}}$

$\mathrm\blue{(25)² = (x)² + (x+5)²}$

$\mathrm\blue{625 = x² + x ² + 10x + 25}$

$\mathrm\blue{625 = 2x² + 10x + 25}$

$\mathrm\blue{2x² + 10x + 25 - 625 = 0}$

$\mathrm\blue{2x² + 10x - 600 = 0}$

$\mathrm\pink{\:now \:divide \:both \:side \:by \:2}$

$\mathrm\blue{\frac{2x²}{2} + \frac{10x}{2} - \frac{600}{2} =\frac{0}{2}}$

$\mathrm\blue{x² + 5x - 300 = 0}$

$\mathrm\pink{\:split \:the \:middle \:term}$

$\mathrm\blue{x² + 20x - 15x - 300 = 0}$

$\mathrm\blue{x( x+20 ) -15 ( x+20 )}$

$\mathrm\blue{( x+20) ( x-15)}$

$\mathrm\pink{\:Now \:the \:x+20 = 0 \:and \:x-15 = 0}$

$\mathrm\pink{x = -20 ( \:minus \:neglected)}$

$\mathrm\pink{x = 15}$

$\mathrm\purple{\:So \:the \:first \:side \:is \:x = 15}$

$\mathrm\purple{\:Second \:side \:is \:x + 5 = 15 + 5 = 20}$

$\mathrm\purple{Ans = 15cm , 20cm}$