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
Answers
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
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