The hypotenuse of right angle triangle is 3root 5cm .if the smaller side is tripled and and larger side is doubled the new hypotenuse will be 15cm.find the sides of the triangle .
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Let the smaller side of the right triangle be x cm and the larger side be y cm. Then,
2 2 2 (3 5)x y [ using Pythagoras theorem] x2 + y2 = 45 ...(1) If the smaller side is tripled and the larger side be doubled, the new hypotenuse is 15 cm. (3x)2 + (2y)2 = (15)2 9x2 + 4y2 = 225 ...(2)
from eqn. (1), we get 2 2 45 . y x Putting this value of y2 in eqn. (2), we get
9x2 + 4 (45 – x2) = 225 5x2 + 180 = 225 5x2 = 45 x2 = 9 x = ± 3 But, length of a side cannot be negative. x = 3 Putting x = 3 in eqn. (1), we get 9 + y2 = 45 y2 = 36 y = ± 6 y = 6 [ y cannot be negative] Hence, the length of the smaller side is 3 cm and the length of the larger side is 6 cm.
2 2 2 (3 5)x y [ using Pythagoras theorem] x2 + y2 = 45 ...(1) If the smaller side is tripled and the larger side be doubled, the new hypotenuse is 15 cm. (3x)2 + (2y)2 = (15)2 9x2 + 4y2 = 225 ...(2)
from eqn. (1), we get 2 2 45 . y x Putting this value of y2 in eqn. (2), we get
9x2 + 4 (45 – x2) = 225 5x2 + 180 = 225 5x2 = 45 x2 = 9 x = ± 3 But, length of a side cannot be negative. x = 3 Putting x = 3 in eqn. (1), we get 9 + y2 = 45 y2 = 36 y = ± 6 y = 6 [ y cannot be negative] Hence, the length of the smaller side is 3 cm and the length of the larger side is 6 cm.
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