What is the value of x, if we have a

Joyce Smith 2021-12-17 Answered
What is the value of x, if we have a triangle, where $$\displaystyle{A}{B}={3}{x}-{5}$$, $$\displaystyle{B}{C}={2}{x}+{20}$$, $$\displaystyle{A}{C}={4}{x}-{30}$$ and the triangle is equilateral?

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Samantha Brown
We have a triangle: $$\displaystyle{A}{B}={3}{x}-{5}$$, $$\displaystyle{B}{C}={2}{x}+{20}$$, $$\displaystyle{A}{C}={4}{x}-{30}$$
An equilateral triangle has the property that all sides have the same length as well as the angles.
Thus, we can pull all the three sides equal to each other:
$$\displaystyle{4}{x}-{30}={3}{x}-{5}$$
$$\displaystyle{4}{x}-{3}{x}=-{5}+{30}$$
$$\displaystyle{x}={25}$$, this is the answer
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Dawn Neal
As we have an an equilateral triangle, we know that all its sides have the same length. This means, we can make them equal to each other and solve for x
$$\displaystyle{4}{x}-{30}={2}{x}+{20}$$
$$\displaystyle{4}{x}-{2}{x}={20}+{30}$$
$$\displaystyle{2}{x}={50}$$
$$\displaystyle{x}={25}$$