Question

☺MATHS ARYABHATTA@@$$



A right triangle has one leg 3 cm longer that the other leg. Its hypotenuse is 3 cm longer than its longer leg. What is the length of the hypotenuse?

Answer 1

let the shortest leg (other leg) of right angle triangle be 'x'

one leg = (x + 3)cm

hypotenuse = (x + 3) + 3 = (x + 6)

by Pythagoras theorem,

(x + 6)^2 = (x)^2 + (x + 3)^2

x^2 + 36 + 12x = x^2 + x^2 + 9 + 6x

x^2 - 6x - 27 = 0

x^2 - 9x + 3x - 27 = 0

x( x - 9) + 3( x - 9) = 0

(x - 9) (x + 3) = 0

x = 9, - 3

length can't be negative, so neglect - 3

. shortest side x = 9cm

hypotenuse = x + 6

= 9 + 6 = 15cm

Answer:
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length of the hypotenuse of right angle triangle = 15cm