Q. 53.7( 3 Votes )

# What is the hypotenuse of the right triangle with perpendicular sides √2 centimetres and √3 centimetres? How much larger than the hypotenuse is the sum of the perpendicular side?

Answer :

__We know that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.__

⇒ In ΔABC, BC^{2} = AB^{2} + AC^{2}

⇒ BC^{2} = (√3)^{2} + (√2)^{2}

⇒ BC^{2} = 3 + 2

⇒ BC^{2} = 5

∴ BC = √5 cm (Hypotenuse)

⇒ √5 ≈ 2.23 cm,

√2 ≈ 1.41 ,

and √3 ≈ 1.73

Sum of perpendicular sides = 1.41 + 1.73 = 3.14 cm

⇒ 3.14 – 2.23 = 0.91 cm

∴ The sum of perpendicular sides is 0.91 cm more than the hypotenuse.

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