Question

PLEASE HELP!!!! PLEASE..

Answer 1

Option A:

ΔDEF $\sim$ ΔABC; x = 1.5; CB = 3.9; AB = 3; $\frac{2}{3}$

Solution:

Each pair of given polygons are similar.

Similarity statement for the given polygons:

In ΔDEF and ΔABC,

∠D = ∠A (Angle)

∠E = ∠B  (Angle)

Therefore, ΔDEF $\sim$ ΔABC (by AA similarity)

If two triangles are similar, then their sides are proportional.

$\Rightarrow \frac{DF}{AC} =\frac{DE}{AB}$

$\Rightarrow \frac{2.4}{3.6} =\frac{2}{2x}$

Do cross multiplication,

⇒ 2.4 × 2x = 2 × 3.6

⇒ 4.8x = 7.2

⇒ x = 1.5

Substitute x = 1.5 in CB and AB,

CB = 3x – 0.6

     = 3(1.5) – 0.6

CB = 3.9

AB = 2x

     = 2(1.5)

AB = 3

Scale factor means ratio of the sides of the triangle.

$\Rightarrow \frac{DF}{AC} =\frac{2.4}{3.6}=\frac{2}{3}$

Therefore, Option A is the correct answer.

Hence ΔDEF $\sim$ ΔABC; x = 1.5; CB = 3.9; AB = 3; $\frac{2}{3}$.