Construct a right triangle whose one side is 3.5 cm and the sum of the other side and the hypotenuse is 5.5 cm.

Question:

Construct a right triangle whose one side is 3.5 cm and the sum of the other side and the hypotenuse is 5.5 cm.

Solution:

Steps of construction:
1. Draw a line segment BC = 3.5 cm

2. Construct $\angle \mathrm{CBX}=90$

3. With B as centre and 5.5 cm radius cut an arc on BX and name it as D. 
4. Join CD. 
5. Construct the perpendicular bisector of CD intersecting BD at point A. 

6. Join AC. 

$\triangle \mathrm{ABC}$ is the required triangle.

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