You can use the <u>determinant</u><u> (square root)</u> of a quadratic equation to determine the number and type of solutions of the equation.
> 0 → 2 real solutions
= 0 → 1 real solution (double root)
< 0 → 2 imaginary(complex) solutions
Using the concept of proportional, it is found that the value of x for the given similar triangles is 2.
<h3>What is a proportion?</h3>A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Since two triangles ΔACD and ΔABE are similar triangles, then their corresponding sides will be proportional.
Therefore, AC/ AB = AD / AE
By substituting the measures of the sides here;
AC/ AB = AD / AE
(x + 10) / 10 = (15 +3) / 15
15(x + 10) = 180
x + 10 = 12
x = 12 - 10
x = 2
Therefore, the value of x for the given similar triangles is 2.
More can be learned about proportions at;
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