A shape is formed by drawing a triangle ABC inside the triangle ADE. BC is parallel to DE.
AB = 4cm BC = xcm DE = x + 3cm DB = x – 4cm Calculate the length of DE.

Answer:

16) C

This involves the use of rule of similarity.

Triangles ABC and ADE are similar.

AB/BC = DA/DE

4/x = x/(x+3)
4x + 12 = x²
x² – 4x – 12 = 0

Factorising, we get:
x² – 6x + 2x – 12
x (x – 6) + 2 (x – 6)
(x – 6) (x + 2)

So x = 6 or x = -2
Since the length cannot be negative, x = 6.

Since DE = x + 3, DE = 6 + 3 = 9 cm.