The length of the hypotenuse of a right triangle is 25 cm .one of it

1.	The length of the hypotenuse of a right triangle is 25 cm .one of its sides is 24 cm. Find the other side ?
Answer» et 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

The length of the hypotenuse of a right triangle is 25 cm .one of its sides is 24 cm. Find the other side ?

Answer»

et 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