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Using ruler and compasses only, construct an ΔABC, given base BC = 7 cm, ∠ABC = 60° and AB + AC = 12 cm.

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(1) Draw a line segment BC = 7cm. 

Using a protractor, 

Draw ∠CBD = 60°. 

Join and extend BD.

(2) Taking B as the center and radius = 12cm, 

Draw an arc, 

Intersecting extended BD at point P. 

Join PC.

(3) Taking P as the center and radius greater than \(\frac{PC}{2}\), 

Draw arcs on each side of PC. 

Now, 

Taking C as the center and same radius, draw arcs, intersecting the previous arcs at points Q and R. 

Join and extend QR.

 Extended QR intersects line segment DB at point A. 

Join AC.

(4) ∆ABC is the required triangle.

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