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Answer :

Given: In \(\triangle{ABC}\) in which BC = 7 cm, \(\angle{B}\) = \(75^\circ\) and AB + AC = 13cm.

Steps of construction:

1. Draw the base BC = 7 cm.

2. At the point B make an \(\angle{XBC}\) = \(75^\circ\).

3. Cut a line segment BD equal to AB + AC = 13 cm from the ray BX.

4. Join DC.

5. Make \(\angle{DCY}\) = \(\angle{BDC}\).

6. Let CY intersect BX at A.

Hence, ABC is the required triangle.

- Construct a \(\triangle{ABC}\) in which BC = 8 cm, \(\angle{B}\) = \(45^\circ\) and AB - AC = 35cm.
- Construct a \(\triangle{ABC}\) in which QR = 6 cm, \(\angle{Q}\) = \(60^\circ\) and PR - PQ = 2cm.
- Construct a \(\triangle{XYZ}\) in which \(\angle{Y}\) = \(30^\circ\), \(\angle{Z}\) = \(90^\circ\) and XY + YZ + ZX = 11cm.
- Construct right triangles whose base is 12 cm and sum its hypotenuse and other side is 18 cm.

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