Question

Which equation could be used to find the value of x if the triangles pictured are congruent by SSS

Answer 1

The equation
`\(4x + 7 = 24\)` represents an equation setting corresponding side lengths equal, but it doesn't directly reflect SSS triangle congruence. Its solution is
`\(x = 4.25\)`.

Sure, the Side-Side-Side (SSS) congruence criterion states that if the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.

Let's analyze the provided equations:

`\(E: 6x - 4\)`

`\(F: 24\)`

`\(G: 4x + 7 = 24\)`

Among these options, the equation
`\(4x + 7 = 24\)` represents an equation setting two expressions involving side lengths equal to each other.

Isolate the variable term:

Subtract 7 from both sides of the equation.

`\[ 4x + 7 - 7 = 24 - 7 \]`

`\[ 4x = 17 \]`

Solve for
`\(x\)`:

Divide both sides of the equation by 4.

`\[ (4x)/(4) = (17)/(4) \]`

`\[ x = (17)/(4) = 4.25 \]`

Therefore, the solution to the equation
`\(4x + 7 = 24\)` is
`\(x = 4.25\)`. However, it's important to note that this equation might not directly represent congruence by SSS for triangles.