Question

Find all values of x that make the triangles congruent. Explain your reasoning.

Answer 1

x =
`(4)/(5),5`

Explanation:

If both the triangles ΔABC and ΔBCD are congruent,

Corresponding sides of both the triangles will be proportional.

`(AB)/(BD)=(AC)/(CD)`

`(5x)/(3x+10)=(5x-2)/(4x+3)`

5x(4x + 3) = (5x - 2)(3x + 10)

20x² + 15x = 15x² + 50x - 6x - 20

20x² + 15x = 15x² + 44x - 20

20x² - 15x² = 44x - 15x - 20

5x² = 29x - 20

5x² - 29x + 20 = 0

5x² - 25x - 4x + 20 = 0

5x(x - 5) - 4(x - 5) = 0

(5x - 4)(x - 5) = 0

`x=(4)/(5),5`