## Related questions with answers

Question

$\triangle A B C \cong \triangle D E F, E F=x^2-7$, and BC=4x - 2. Find the values of x.

(A) -1 and 5

(B) -1 and 6

(C) 1 and 5

(D) 2 and 3

Solution

VerifiedStep 1

1 of 2Given that $\triangle ABC\cong\triangle DEF$, then $\overline{BC}\cong \overline{EF}$ by CPCTC:

$BC=EF$

$4x-2=x^2-7$

$0=x^2-4x-5$

Factor the right side:

$0=(x+1)(x-5)$

By zero product property,

$x=-1,5\color{white}\tag{1}$

So, the correct answer is choice $\textbf{\color{#c34632}A.}$

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