The length of side x in simplest radical form with a rational denominator is 8√3
<h3>How to find the length of side x in simplest radical form with a rational denominator?</h3>
The given parameters are:
Triangle type = Equilateral triangle
Height (h) = 12
Missing side length = x
The missing side length, x is calculated using the following sine ratio
sin(60) = Height/Missing side length
This gives
sin(60) = 12/x
Make x the subject of the formula
So, we have
x = 12/sin(60)
Evaluate the quotient
So, we have
x = 12/(√3/2)
This gives
x = 24/√3
Rationalize
x = 24/√3 * √3/√3
Evaluate
x = 8√3
Hence, the length of side x in simplest radical form with a rational denominator is 8√3
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It would be 2(x+3)(x+1)=0
Explanation:
I used factor by grouping. You multiply the first term (2) by the last term (6). This gives you 12 then take the factors of 12 that add up to the middle term 8. You get 6 and 2.
It should look like 2x^2+6x+2x+6=0
when you do factor by grouping you factor the first two terms and then the last two terms separately. So you get (2x+2) and (x+3). (2x+2) could be factored into 2(x+1). Then you put everything together and get 2(x+3)(x+1)=0