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Question

Construct a quadrilateral ABCD such that the sum of the opposite sides are 8 cm and 11.2 cm, and each angle is a right angle. 


Your Answer
A
Correct Answer
B
Your Answer
C
Your Answer
D
Data insufficient

Solution

The correct option is B
Given each angle is a right angle and the sum of the opposite sides are 8 cm and 11.2 cm

Hence, the quadrilateral is a rectangle.

If the following figure is the rough sketch, AD=BC and AB=CD

If, AD + BC = 8 then,
2×AD=8cm
AD=82=4cm
AD=BC=4cm

If, AB + BC = 11.2 then, 2×AB=11.2cm
AB=11.22=5.6cm
AB=CD=5.6cm

Steps of Construction:

Step 1: Draw a line segment AB of length 5.6 cm.

Step 2: At A and B, construct 90° and extend the lines.

Step 3: Keeping A and B as the centers, draw two arcs of radius 4cm on both the points. Mark the point D and C respectively.

Step 4: Join D and C to get the complete quadrilateral. 

We get the required quadrilateral as follows. 

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