Question

If Triangle ABC is congruent to Triangle SRT, find the possible value(s) for x

Answer 1

x = 2 or x = -3

Explanation:

Given that ∆ABC ≅ ∆SRT, it follows that their corresponding side lengths are congruent to each other.

Thus:

`RT = BC`

`(x^2 + x) = 6`

Solve for x

`x^2 + x = 6`

Subtract 6 from each side

`x^2 + x - 6 = 6 - 6`

`x^2 + x - 6 = 0`

Factorise

`x^2 + 3x - 2x - 6 = 0`

`x(x + 3) -2(x + 3)`

`(x - 2)(x + 3)`

x = 2 or x = -3