The length of the sides of a right angled triangle are ym, (3y-1) m and (3y+1) m, find y

Answer 1

To find y, we can use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

So, we have:

y^2 + (3y-1)^2 = (3y+1)^2

Expanding and simplifying:

y^2 + 9y^2 - 6y + 1 = 9y^2 + 6y + 1

Combining like terms:

10y^2 - 6y = 9y^2 + 6y

Rearranging the equation:

10y^2 - 6y = 9y^2 + 6y

Subtracting 9y^2 from both sides:

y^2 - 6y = 6y

Subtracting 6y from both sides:

y^2 - 6y - 6y = 0

y^2 - 12y = 0

Factoring out y:

y(y - 12) = 0

Setting each factor to zero:

y = 0 or y = 12

Since the sides of a triangle cannot be zero, the only valid solution is y = 12.