x^2 + 12^2 = (3x)^2?

Question

its a right triangle, and its very hard.

Answer 1

x^2 + 12^2 = (3x)^2 → x^2 + 144 = 9*x^2 → 8*x^2 = 144 → x^2 = 18 → x = √¯¯18 = 3√¯¯2 ≈ 4.243
So the triangle's sides are 3√¯¯2 , 12, 9√¯¯2.

Answer 2

This answer uses as much algebra as possible, instead of arithmetic.

x^2 + 12^2 = (3x)^2?

Distributive Property on the right side:

x^2 + 12^2 = 3^2 * x^2

12^2 = 3^2 * x^2 - x^2

Distributive Property again:

12^2 = x^2 ( 3^2 - 1 )

x^2 = 12^2 / (3^2 - 1)

x =+/- sqrt(12^2 / (3^2 - 1) )

x =+/- 12 / sqrt( 3^2 - 1 )

Difference of two squares

x =+/- 12 / sqrt ( (3+1) * (3-1) )

x =+/- 12 / sqrt ( (4) * (3-1) )

x =+/- 12 / (2 * sqrt (3-1) )

x =+/- 6 / sqrt (3-1)

x =+/- 6 / sqrt (2)

x =+/- 6 / (2 ^ 1/2)

Multiply numerator and the denominator by the denominator

x =+/- ( 6 (2 ^ 1/2) ) / (2 ^ 1/2) ^ 2

x =+/- ( 6 (2 ^ 1/2) ) / 2

x =+/- 3 (2 ^ 1/2)

Very simple using only algebra, in only 15 steps.

Answer 3

It's not hard:

x squared + 144 = 9x squared
144 = 8x squared
18 = x squared
x = 18 to the half power or -18 to the half power
x = 3 square roots of 2 or -3 square roots of 2

Answer 4

take x^2 to the right

12^2 = (3x)^2-x^2 = 8x^2
devide my 8 on both sides

x^2 = 12^2/8 = 144/8 = 18 = (3*sqrt(2))^2

take square root x = 3 sqrt(2) or - 3sqrt(2)

Answer 5

Divide through by x^2:

1 + (12/x)^2 = 9

This means (12/x)^2 = 8, or 12/x = sqrt(8) = 2 sqrt(2). So x = 12/(2 sqrt (2)) = 3 sqrt(2). If you require integer solutions, there are none.

Answer 6

x=3*2^(1/2)

Answer 7

assuming nothing it mistyped

x^2 + 12^2 = (3x)^2
x^2 + 144 = (3x)^2
x^2 + 144 = 9x^2
8x^2 + 144
x^2 = 18
x = sqrt(18)
x = -3sqrt(2) or 3sqrt(2)

the sides are 18, 12, and 54

Answer 8

x^2 + 144 = 9x^2 => 144 = 8x^2 => 18 = x^2 => x = 3sqrt (2).

Answer 9

x^2 + 144 = 9x^2

144 = 8x^2

18 = x^2

x = 18^(1/2) or -18^(1/2)

x = 3sqrt(2) or -3sqrt(2)

Answer 10

x^2+144=9x^2
so 8x^2=144
x^2=18
x=sqrt(18)