Question

In the given figure De parallel to BC BP and CP are bisector of Angle B and angle C respectively if BD is equal to cm and ac is equal to 3 cm then the is equal to

Answer 1

Answer:

5 cm

Step-by-step explanation:

Answer 2

• The length of DE is equal to 5 cm .

Given :- In the given figure, DE || BC . BP and CP are bisectors of ∠B and ∠C respectively. BD = 2 cm and CE = 3 cm .

To Find : Length of DE = ?

Solution :-

Since DE || BC,

→ ∠DPB = ∠PBC { Alternate angles } ---- Equation (1)

And, BP is angles bisector of ∠B,

→ ∠DBP = ∠PBC ------ Equation (2)

using Equation (1) and Equation (2) in ∆DPB we get,

→ ∠DPB = ∠DBP

So,

→ BD = DP { Sides opposite to equal angles are equal in length.} ------- Equation (3)

Similarly we can conclude that,

→ ∠EPC = ∠ECP

So,

→ CE = PE ----------- Equation (4)

Adding Equation (3) and Equation (4) we get,

→ BD + CE = DP + PE

→ BD + CE = DE

putting given values of BD = 2 cm and CE = 3 cm we get,

→ 2 + 3 = DE

→ 5 = DE

→ DE = 5 cm (Ans.)

Hence, length of DE is equal to 5 cm .

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