Question

To construct a $△$ABC in which BC = $10$ cm and B= ${60}^o$and AB + AC =14 cm, then the length of BD used for construction

• A. $7$ cm
• B. $14$ cm
• C. $20$ cm
• D. $10$ cm

Answer 1

The correct option is B $14$ cm

Construction:

A]. Draw the base BC and at the point, B makes an angle, say $XBC$ equal to the given angle.

B]. Cut a line segment $BD$ equal to $AB+AC$ from the ray $BX$.

C]. Join $DC$ and make an angle $DCY$ equal to $BDC$.

D]. Let $CY$ intersect $BX$ at $A$

E]. $ABC$ is the required triangle.

F]. In triangle $\Delta ACD$, $\angle ACD=\angle ADC$.

G]. So, $AB=BD–AD=BD–AC$

H]. $AB+AC=BD$

From this we get, $BD=14cm$.