Question

The hypotenuse of a right- angled triangle is 3√5cm.if the larger side is twice the smaller side. Find the length of the larger side.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let the smaller side of the right triangle be x cm and the larger side by y cm.

Then, x

2

+y

2

=(3

5

)

2

⇒x

2

+y

2

=45....(i)

If the smaller side is tripled and the larger side be doubled, the new hypotenuse is 15cm.

∴(3x)

2

+(2y)

2

=15

2

⇒9x

2

+4y

2

=225...(ii)

From equation (i) we get y

2

=45−x

2

Putting y

2

=45−x

2

in equation (ii), we get

9x

2

+4(45−x

2

)=225⇒5x

2

+180=225⇒5x

2

=45⇒x

2

=9⇒x=±3

But length of a side cannot be negative. Therefore x=3

Putting x=3 in (i) we get

9+y

2

=45⇒y

2

=36⇒y=6

Hence, the length of the smaller side is 3cm and the length of the larger side is 6cm.