Question

the hypotenuse of a right angled triangle is 3√5 cm if the smaller side is tripled and the larger side is doubled the new hypotenuse becomes 15 cm find the length of each side of triangle

Answer 1

hope this will help you

Answer 2

Answer:

The length of smaller side of right angled triangle is 3 cm and larger side is 6 cm.

Step-by-step explanation:

The smaller side of right angled triangle be x and larger side be y.

The hypotenuse of a right angled triangle is 3√5 cm.

Using Pythagoras theorem

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

$x^2+y^2=45$                 ..... (1)

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

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

$9x^2+4y^2=225$            ..... (2)

Multiply equation (1) by 9.

$9x^2+9y^2=405$                 ..... (3)

Subtract equation (2) from (3).

$5y^2=180$

$y=36$

$y=6$

Put this value it equation (1).

$x^2+(6)^2=45$

$x^2=9$

$x=3$

Therefore the length of smaller side of right angled triangle is 3 cm and larger side is 6 cm.