Find the value of x. Round u'r answer to the nearest hundredth, if necessary.
Area of triangle=108m^2
A=1/2 bh
b=(x+6)m
h=xm
So, 108m^2=1/2 ((x+6)m)(xm)
108m^2=1/2 m^2+x^2+6????
If so then what? Sub m^2 from the left side?? Then what? :/
I think the m means meters, as in unit of length: 6m
108 = 1/2 (x+6)(x)
x^2+6x-216 = 0
(x-18)(x+12) = 0
since we want a positive side, x=18m
If you really want to carry the m's along, just do so:
108m^2 = 1/2 (x+6)m*xm
= 1/2 x(x+6)m^2
Now the m^2's cancel out, and we proceed as at first.
To find the value of x, we can solve the equation step by step. Let's start with the equation:
108m^2 = 1/2 m^2 + x^2 + 6
To simplify the equation, we can get rid of the fraction by multiplying the entire equation by 2:
(108m^2) * 2 = (1/2 m^2 + x^2 + 6) * 2
216m^2 = m^2 + 2x^2 + 12
Next, we can subtract m^2 from both sides of the equation to isolate the variables:
216m^2 - m^2 = m^2 - m^2 + 2x^2 + 12
215m^2 = 2x^2 + 12
Now, let's isolate the term with x^2 by subtracting 12 from both sides:
215m^2 - 12 = 2x^2 + 12 - 12
215m^2 - 12 = 2x^2
Finally, to isolate x, divide both sides of the equation by 2:
(215m^2 - 12) / 2 = (2x^2) / 2
107.5m^2 - 6 = x^2
To find x, we need to take the square root of both sides:
√(107.5m^2 - 6) = √(x^2)
±√(107.5m^2 - 6) = x
Therefore, the value of x is ±√(107.5m^2 - 6).