Length of AB = 18. 92
Length of AC = 26. 15
Length of BC = 32. 552
Using the Pythagorean theorem, we have that
[tex](20 x-2)^2 = (12x + 20)^2 + (25x)^2[/tex]
Expand the bracket
[tex]400x^2- 4 = 144x^2 + 400 + 625x^2[/tex]
Collect like terms
[tex]400x^2 - 144x^2 - 625x^2 = 400 + 4[/tex]
[tex]-369x^2 = 404[/tex]
Make x^2 subject
[tex]x^2 = \frac{404}{369}[/tex]
[tex]x = \sqrt{1.0948}[/tex]
[tex]x = 1. 046[/tex]
Thus,
Length of AB = 20x -2 = 20(1. 046) - 2 = 18. 92
Length of AC = 25x = 25* 1.046 = 26. 15
Length of BC = 12x + 20 = 12(1. 046) + 20 = 32. 552
Learn more about isosceles triangles here:
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