Question

ABCD is a trapezium in which AB || DC and E, F are points on AD and BC respectively such that EF || DC. If ED = 36 cm, BF = 70 cm and FC = 30 cm, then the length of AD is :

• A. 124 cm
• B. 120 cm
• C. 110 cm
• D. 114 cm

Hint:

Always read carefully whether the question asks for the missing segment (\(AE\)) or the entire side (\(AD\)).
Here, \(AE = 84 \text{ cm}\) is not the final answer; we must add \(36 \text{ cm}\) to get \(120 \text{ cm}\).

Answer 1

The Correct Option is B

Step 1: Set up the ratio from the intercept theorem.
Since $EF \parallel DC \parallel AB$, the line $EF$ divides the non-parallel side in the ratio $\frac{AE}{ED} = \frac{BF}{FC} = \frac{70}{30} = \frac{7}{3}$.
Step 2: Convert straight to a whole-side ratio.
Instead of finding $AE$ first, write $\frac{AD}{ED} = \frac{AE+ED}{ED} = \frac{7}{3}+1 = \frac{10}{3}$.
Step 3: Solve directly for AD.
\[ AD = \frac{10}{3} \times ED = \frac{10}{3} \times 36 \]
\[ \boxed{120 \text{ cm}} \]