Hello, Lewis1!

A shape is formed by drawing a triangle ABC inside the triangle ADE.

BC is parallel to DE.

AB = 4cm, BC = x cm, DE = x + 3 cm, DB = x - 4 cm

Calculate the length of DE.

The correct answer is 9 cm. Code:

A
o
4 * *
* *
* *
B o * * * o C
* x *
x - 4 * *
* *
D o * * * * * o E
x + 3

We have: .∆ABC ~ ∆ADE

- - - . . . BC . . .DE . . . . . .x . . .x + 3

Hence: . --- .= .--- . .→ . . -- .= .------

- - - . . . BA . . .DA . . . . . .4 . . . . x

. . x^2 .= .4x + 12 . . → . . x^2 - 4x - 12 .= .0

. . (x - 6)(x + 2) .= .0 . . → . . x ,= ,6, -2

Hence: .x = 6

Therefore: .DE .= .x + 3 .= .9