Using proportions, the lengths of the unknown sides are given as follows:
- 2x = 10.
- x - 3 = 2.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the triangles are similar, hence the lengths of it's sides follow the proportion given next:
Applying cross multiplication:
2x(x - 3) = 20
2x² - 6x - 20 = 0
x² - 3x - 10 = 0
(x - 5)(x + 2) = 0.
Then the positive solution is:
x - 5 = 0 -> x = 5.
And the lenghts are:
- 2x = 10.
- x - 3 = 2.
More can be learned about proportions at brainly.com/question/24372153
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