Question

the hypotenuse of a right angled triangle is 3√10. If the smaller side is tripled and the longer side is doubled,new hypotenuse will be 9√5. How long are the sides of the trianhle

Answer 1

x²+y²=(3√10)²
x²+y²=90
y²=90-x²...(i)

(3x)²+(2y)²=(9√5)²
9x²+4y²=405

from eq (i)
9x²+4(90-x²)=405
9x²+360-4x²=405
5x²-45=0
5(x²-9)=0
x²-9=0
x=√9
x= positive and negative 3
lenght of side cannot be negative. therefore x=3

y²=90-(3)²
    =90-9
    =81 
y=9

the length of smaller side is 3 cm and length of larger side is 9 cm.

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