Question

c) triangle abc with sides: ab = 7, bc = 9, ac = x + 11. triangle def with sides: de = 2y - 5, ef (length not fully visible), df = 3x - 13. (note: the image shows two triangles, likely congruent, with labeled sides containing variables x and y.)

Explanation:

Step1: Assume triangles are congruent (sides equal)

Assume \(\triangle ABC \cong \triangle DEF\) (implied by diagram, so corresponding sides equal). So \(AC = EF\), \(AB = DE\), \(BC = DF\). Let's first solve for \(x\) using \(AC = EF\). \(AC = x + 11\), \(EF = 3x - 13\). Set equal: \(x + 11 = 3x - 13\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(11 = 2x - 13\). Add 13 to both sides: \(24 = 2x\). Divide by 2: \(x = 12\).

Step3: Solve for \(y\) using \(AB = DE\)

\(AB = 7\), \(DE = 2y - 5\). Set equal: \(2y - 5 = 7\). Add 5: \(2y = 12\). Divide by 2: \(y = 6\). (If needed, check \(BC = DF\): \(BC = 9\), \(DF\) would be consistent with congruence, but we solved \(x,y\) from sides.)

Answer:

\(x = 12\), \(y = 6\) (assuming congruent triangles, solving for variables in side lengths)