Question

Geometry question, need help!

Answer 1

Answer:

x = 7.5

Step-by-step explanation:

We first labelled the diagram we get

DC = 8

AD = 10

CE = 6

BE = x

∴ AC =AD + DC = 18

∴ BC = BE + ED = x + 6

To Find :

BE = x =?

Solution:

Let DE || AC

In  Δ ABC and Δ DEC

∠A ≅ ∠D    …………..{corresponding angles ∵ DE || AB }

∠B ≅ ∠E      ..............{corresponding angles ∵ DE || AB }

∠C ≅ ∠C    ……….....{Reflexive Property}    

Δ ABC ~ Δ DEC ….{Angle-Angle-Angle  Similarity test}

If two triangles are similar then their sites are in proportion.

$\frac{AB}{DE} =\frac{BC}{EC} =\frac{AC}{CD}\ \textrm{corresponding sides of similar triangles are in proportion}$

On substituting the given values we get

∴ $\frac{8}{18} = \frac{6}{6+x} \\\\8(6+x) = 6\times 18\\\\\textrm{using distributive property we get}\\48+8x=108\\8x=108-48\\x=\frac{60}{8}\\ \\x=7.5\\\\\therefore x =7.5$