Respuesta :

gmany

ΔBED and Δ DEC are similar (AAA). Therefore we have the proportion:

[tex]\dfrac{a}{18}=\dfrac{4}{a}[/tex]      cross multiply

[tex]a^2=(18)(4)\\\\a^2=72\to a=\sqrt{72}\\\\a=\sqrt{36\cdot2}\\\\a=\sqrt{36}\cdot\sqrt2\\\\\boxed{a=6\sqrt2}[/tex]

The value of a is 6√2 .

How to find the side of a triangle from concept of similar triangle -

In ΔBED and ΔEDC , we have

  • ED = ED (Common side)
  • ∠BED = ∠DEC (Both the angles are equal and have value 90°)
  • ∠BDE = ∠EDC (Perpendicular bisector so the base angles are equal)

We have,  ΔBED ≅ ΔEDC (Angle-Side-Angle axiom)

Now using the proportion axiom as both the triangles are congruent.

   [tex]\frac{BE}{ED} = \frac{ED}{EC}[/tex]

⇒ [tex]\frac{18}{a} = \frac{a}{4}[/tex]

⇒ [tex]a^{2} = 72[/tex]

∴ [tex]a = \sqrt{72} = 6\sqrt{2}[/tex]

Using basic proportionality axiom, we find the value of a as 6√2 .

To learn more about properties Similar triangles, refer -

https://brainly.com/question/1799826

#SPJ2

Otras preguntas