Question

In the construction of a triangle $ABC$ in which $BC=6cm$, ∠$B=60°$ and $AB+AC=14cm$, the length of $BD$ is.

• A. $7cm$
• B. $12cm$
• C. $14cm$

Answer 1

The correct option is C $14cm$

Construction steps:
1. Draw the base BC of the given length.
2. Construct ∠B = 60°.
3. Mark a point D on this ray such that BD = AB + AC = 14 cm. Join DC.
4. Draw the perpendicular bisector of DC to intersect DB at A.
5. Join AC. ABC is the required triangle.
From step 3, we get BD = 14 cm.

Alternatively, consider the following:

△AMC ≅ △AMD (By SAS congruency)
∴ AC = AD (By CPCT)
Hence,
BD = AB + AD = AB + AC = 14 cm