Question

The hypotenus of a right triangle is 3 root 5.If the smaller side is tripled and the larger side is doubled, the new hypotenus will be 15cm.Find the length of each side?

Answer 1

Answer:

3cm & 6 cm

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Step-by-step explanation:

Let say smaller side = x

Larger side = y

hypotenus^2 = x^2 + y^2

(3√5)^2 = x^2 + y^2

45 = x^2 + y^2    EqA

Now

(15)^2 = (3x)^2 + (2y)^2

225 = 9x^2 + 4y^2   Eq B

Now Eq A is multiplied by 4 ans subtracting from EqB

225 - 4*45 = 9x^2 - 4x^2  + 4y^2 - 4y^2

225-180 = 5x^2

45 = 5x^2

9 = x^2

3 = x   ( as x can not be negative)

smaller side = 3 cm

Larger side = 2x = 2*3 = 6 cm

Hypotenus already given = 3√5 cm