Question

Solve for x in triangle and explain please

Answer 1

• x = 5

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Parallel lines cut transversals proportionally.

We got equal ratios:

• 6/(x - 1) = (x - 2)/2
• (x - 1)(x - 2) = 6*2
• x² - 3x + 2 = 12
• x² - 3x - 10 = 0
• x² - 5x + 2x - 10 = 0
• x(x - 5) + 2(x - 5) = 0
• (x + 2)(x - 5) = 0
• x + 2 = 0 and x - 5 = 0
• x = - 2 and x = 5

x = - 2 doesn't work as it reveals a negative side length, so the answer is x = 5.