In the diagram above. |AB| = 12cm, |AE| = 8cm, |DCl = 9cm and AB||DC. Calculate |EC|
Attached Figure / Diagram
A
10cm
B
9cm
C
8cm
D
7cm
E
6cm
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
|AB| = 12 cm; |DC| = 9 cm; |AE| = 8 cm.
\(\Delta\) ABE and \(\Delta\) EDC are similar triangles. Hence,
\(\frac{|AB|}{|DC|} = \frac{|AE|}{|EC|}\)
\(\frac{12}{9} = \frac{8}{|EC|}\)
\(\therefore |EC| = \frac{9 \times 8}{12}\)
= 6 cm
Source: Myschool Past Questions Archive (Record #23734)