Question

The hypotenuse of a right angled triangle is 5 meter. If smaller side is doubled and other side is increased to three times, hypotenuse becomes 6√5 meters. Find the sides of triangle​

Answer 1

Solution :-

Let us assume that, smaller side of right angled triangle is x m and other side is y m.

Now,

→ Length of hypotenuse = 5m .

According to pythagoras theorem,

→ x² + y² = 5²

→ x² + y² = 25 ----------- Eqn.(1)

Now, given that, smaller side is doubled and other side is increased to three times, hypotenuse becomes 6√5 meters .

So,

→ smaller side is tripled = 2x

→ other side is doubled = 3y

→ New hypotenuse = 6√5 m .

According to pythagoras theorem,

→ (2x)² + (3y)² = (6√5)²

→ 4x² + 9y² = 180

→ 4x² + 4y² + 5y² = 180

→ 4(x² + y²) + 5y² = 180

Putting value of Eqn.(1) now,

→ 4*25 + 5y² = 180

→ 100 + 5y² = 180

→ 5y² = 180 - 100

→ 5y² = 80

→ y² = 16

→ y = ± 4 .

( Negative value of side is not Possible).

Therefore,

→ y = 4m.

Putting value of y in Eqn.(1) now,

→ x² + 4² = 25

→ x² = 25 - 16

→ x² = 9

→ x = 3m.

Hence, Smaller side of right angled triangle is 3m and other side is 4m.

Learn More :-

in ∆ABC, a=3,b=4,c=5 , then find distance between incentre and circumcentre

https://brainly.in/question/22103570

Answer 2

Solution :-

Let us assume that, smaller side of right angled triangle is x m and other side is y m.

Now,

→ Length of hypotenuse = 5m .

According to pythagoras theorem,

→ x² + y² = 5²

→ x² + y² = 25 ----------- Eqn.(1)

Now, given that, smaller side is doubled and other side is increased to three times, hypotenuse becomes 6√5 meters .

So,

→ smaller side is tripled = 2x

→ other side is doubled = 3y

→ New hypotenuse = 6√5 m .

According to pythagoras theorem,

→ (2x)² + (3y)² = (6√5)²

→ 4x² + 9y² = 180

→ 4x² + 4y² + 5y² = 180

→ 4(x² + y²) + 5y² = 180

Putting value of Eqn.(1) now,

→ 4*25 + 5y² = 180

→ 100 + 5y² = 180

→ 5y² = 180 - 100

→ 5y² = 80

→ y² = 16

→ y = ± 4 .

( Negative value of side is not Possible).

Therefore,

→ y = 4m.

Putting value of y in Eqn.(1) now,

→ x² + 4² = 25

→ x² = 25 - 16

→ x² = 9

→ x = 3m.

Hence, Smaller side of right angled triangle is 3m and other side is 4m.

Learn More :-

in ∆ABC, a=3,b=4,c=5 , then find distance between incentre and circumcentre

brainly.in/question/22103570