Find an expression for the length of the base of the triangle

Question

Triangle: Find an expression for the length of the base of the triangle ABC.

c=10cm a=2x-2 b=2x

Answer 1

Use the Pythagorean Theorem, a² + b² = c².

Let a = 2x - 2, b = 2x, and c = 10. Then we have the following:

(2x - 2)² + (2x)² = (10)²

4x² - 4x - 4x + 4 + 4x² = 100

8x² - 8x + 4 = 100

8x² - 8x - 96 = 0

x² - x - 12 = 0

Factor the equation from above to find any solutions. Find two factors that multiply to get -12 and add up to -1.

1, -12

-1, 12

2, -6

-2, 6

3, -4

-3, 4

(x + 3)(x - 4) = 0 ⇒ x + 3 = 0 or x - 4 = 0 ⇒ x = -3 or x = 4. Since the length can't be a negative, the only solution that will work is x = 4.

a = 2(4) - 2 = 8 - 2 = 6 cm

b = 2(4) = 8 cm