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klio [65]
3 years ago
9

Order the side lengths from least to greatest

Mathematics
1 answer:
Liula [17]3 years ago
7 0

Answer:

BC < CE < BE < ED < BD

Step-by-step explanation:

In the triangle BCE,

m∠BEC + m∠BCE + m∠CBE = 180°

m∠BEC + 81° + 54° = 180°

m∠BEC = 180 -  135

m∠BEC = 45°

Order of the angles from least to greatest,

m∠BEC < m∠CBE > mBCE

Sides opposite to these sides will be in the same ratio,

BC < CE < BE ----------(1)

Now in ΔBED,

m∠BEC + m∠BED = 180°

m∠BED = 180 - 45

             = 135°

Now, m∠BDE + m∠BED + DBE = 180°

11° + 135°+ m∠DBE = 180°

m∠DBE = 180 - 146

             = 34°

Order of the angles from least to greatest will be,

∠BDE < ∠DBE < ∠BED

Sides opposite to these angles will be in the same order.

BE < ED < BD ----------(2)

From relation (1) and (2),

BC < CE < BE < ED < BD

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