Question

8. The hypotenuse of a right angled
triangle is 25 cm and the difference
in lengths of the other two sides is 5 cm
write a quadratic equation to find the
length of the other sides.​

Answer 1

Answer:

300cm2(square cm)

Step-by-step explanation:

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=300cm2(square cm)