Question

Geometry question, need help!

Answer 1

x = 7.5

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 ………….. AB

∠B ≅ ∠E ..............

∠C ≅ ∠C ……….....{Reflexive Property}

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

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

`(AB)/(DE) =(BC)/(EC) =(AC)/(CD)\ \textrm{corresponding sides of similar triangles are in proportion}\\`

On substituting the given values we get

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