Question

which of the following statements is incorrect? a fe = 58 b de = 58 c x = 8 d df = 40

Explanation:

Step1: Assume the triangle is isosceles

If we assume \(DF = DE\), then \(8x - 24=40\).
Solve the equation \(8x - 24 = 40\):
Add 24 to both sides: \(8x=40 + 24\), so \(8x=64\).
Divide both sides by 8: \(x = 8\).

Step2: Calculate the length of \(FE\)

Substitute \(x = 8\) into the expression for \(FE=6x + 10\).
\(FE=6\times8+10=48 + 10=58\).

Step3: Analyze each option

• Option A: \(FE = 58\) (correct as calculated above).
• Option B: \(DE = 40

eq58\) (incorrect).

• Option C: \(x = 8\) (correct from step 1).
• Option D: \(DF=40\) (given).

Answer:

B. \(DE = 58\)