Question

The length of the hypotenuse of a right triangle is 25 cm

.one of its sides is 24 cm. Find the other side ?​

Answer 1

⇒  Let one of the side be x and the other be x+5

By Pythagoras theorem,

(25)  

2  =x  ^2  +(x+5)  ^2  

⇒  625=x  ^2 +x ^ 2  +10x+25

⇒  625=2x^2  +10x+25

⇒  2x^2 +10x−600=0

⇒  x^2 +5x−300=0

⇒  x^2 +20x−15x−300=0

⇒  x(x+20)−15(x+20)=0

⇒  (x+20)(x−15)=0

⇒  x+20=0 and x−15=0

∴  x=−20 and x=15

But x cannot be negative.

⇒  Hence, one side =x=15cm

⇒  Other side x+5=15+5=20cm

⇒  The product of the length of sides =15cm×20cm=300cm  

2

Answer 2

$let \: abc \: is \: a \: right \: angle \: triangle \: \\ where \: ab \: = base = 24 \: cm \: \\ ac = hypoteneus \: = 25cm \: \\ bc = perpendicular=? \\ by \: using \: pythagoras \: theorum \: \\ = > {ab}^{2} + {bc}^{2} = {ac}^{2} \\ = > {24}^{2} + {bc}^{2} = {25}^{2} \\ = > 576 + {bc}^{2} = 625 \\ = > {bc}^{2} = 625 - 576 \\ = > {bc}^{2} = 49 \\ = > bc = \sqrt{49} \\ = > bc = 7 \: cm \\ therefore, \: the \: lenght \: of \: other \: side \: is \: 7 \: cm$