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1 year ago

The triangle below is equilateral. Find the length of side xx in simplest radical form with a rational denominator.

Mathematics

1 answer:

mylen [45]1 year ago

6 0

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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Answer:

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Step-by-step explanation:

Let the three multiples be 6x, 6(x+1) and 6(x+2) respectively.

6x+6(x+1)+6(x+2)=162

6x+6x+6+6x+12=162

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Therefore, the three multiples are 6(8), 6(8+1) and 6(8+2)

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geniusboy [140]

Answer:

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Step-by-step explanation:

So the question here is asking you to use the quadratic formula which is expressed as: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\$

A quadratic can generally be expressed as: $y=ax^2+bx+c$

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We can identify the following values: a=1, b=-5, c=-1

Btw the equation explicitly write "1" as the coefficient of x, but since it's not provided it's implied that it's 1.

So plugging in the known values, we get the following equation:

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The last step just consists of taking the + and - solution, and since it asks for exact solutions you leave the 29 under the radical, and you don't approximate. There is no further simplification that can be done here.

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