Question

The hypotenuse of a right triangle is 3 root 10 cm. If the smaller leg is tripled and the longer leg doubled , new hypotenuse will be 9 root 5 cm , is it possible to draw such a right triangle? If so, how long are the legs of the triangle? (I need an answer that has quadratic equation in it.)

Answer 1

length of hypotenuse= 3√10
 according to Pythagoras theorem:
x² + y²= (3√10)²= 90

The smaller side is tripled so= 3x
The larger side is doubled = 2y
new hypotenuse= 9√5

now: (3x)² + (2y)²= (9√5)²
9x² + 4y² = 405
5x² + 4x² + 4y² = 405
5x² +4 (x²+y²) = 405
5x² + 4(90)= 405
5x²= 45
x²= 45/5
x= 3

Putting the value of x in starting eq we get y= 9 

Answer 2

Hey mate here is your answer!!