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The hypotenuse of a right triangle is $3 \sqrt{5} cm$ If the smaller side is tripled and the

larger side is doubled, the new hypotenuse will be 15 cm. Find the length of each side

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An Intiative by Sri Chaitanya

y = 6

y = 5

y = 2

y = 4

answer is A.

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Detailed Solution

Given, length of hypotenuse=

3 \sqrt{5} cm

The new hypotenuse = 15 cm
Suppose the right triangle's smaller side = x cm
And its larger side = y cm.
Then, according to Pythagoras Theorem,

x^{2} + y^{2} = (3 \sqrt{5})^{2}

x^{2} + y^{2} = 45

y^{2} = 45 - x^{2}

When smaller side is tripled while the larger side be doubled, then the new hypotenuse become 15 cm. So,

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

9 x^{2} + 4 y^{2} = 225

………………..(1)
Substitute

y^{2} = 45 - x^{2}

in equation (1) as,

9 x^{2} + 4 (45 - x^{2}) = 225

\Rightarrow 5 x^{2} + 180 = 225

\Rightarrow 5 x^{2} = 45

\Rightarrow x^{2} = 9

\Rightarrow x = \pm 3

But length of a side always positive.
Therefore

x = 3

Substitute x = 3 in equation (1)

9 + y^{2} = 45

\Rightarrow y^{2} = 36

\Rightarrow y = 6

Hence, the length of the smaller side= 3 cm The length of the larger side =6 cm.
The Correct Answer is 1.

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