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<u>Given</u>:
Given that the figure of similar triangles.
The altitude of the triangle is x.
The length of the left part is 30.
The length of the right part is 15.
We need to determine the value of x.
<u>Value of x:</u>
The value of x can be determined using the geometric mean theorem.
Thus, we have;
Substituting the values, we have;
Cross multiplying, we get;
Taking square root on both sides, we have;
Thus, the value of x is 15√2
Inequalities help us to compare two unequal expressions. There exists no solution to the given set of inequalities.
<h3>What are inequalities?</h3>Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given Inequalities can be solved as,
5 - x > 7
-x > 7 - 5
-x > 2
x < -2
2x + 3 ≥ 13
2x ≥ 10
x ≥ 5
As per the solution of the two inequalities, the value of x should be less than -2 but at the same time, it should be more than or equal to 5, which is impossible. Thus, there is no solution for the given inequalities.
This can be confirmed by graphing the two inequalities, as shown below. Since there is no area in common between the two inequalities, there exists no solution to the given set of inequalities.
Learn more about Inequality:
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