Question

Solve for x, please help finals are in a day and I have a D in this class(Geometry)

Answer 1

x = 2

Explanation:

• In order to find the value of x, first we need to prove ∆ABC and ∆ADE as similar ∆s.

• So, let's prove:

• In ∆ABC and ∆ADE,

• 
  `\angle ABC \cong \angle ADE....(each \: 90\degree)`

• 
  `\angle BAC \cong \angle DAE....(common \: \angle s)`

• 
  `\implies \triangle ABC \sim \triangle ADE` (By AA postulate)

• 
  `\implies (AB)/(AD)=(BC)/(DE)....(csst)`

• 
  `\implies (2)/(2+x)=(1)/(2)`

• 
  `\implies {2+x}=4`

• 
  `\implies {x}=4-2`

• 
  `\implies {x}=2`