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.

• A.
• B.
• C.
• D. Data insufficient

Answer 1

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$\times AD=8cm$
$\Rightarrow AD=\frac{8}{2}=4cm$
$\therefore AD=BC=4cm$

If, AB + BC = 11.2 then, $2\times AB=11.2cm$
$\Rightarrow AB=\frac{11.2}{2}=5.6cm$
$\therefore AB=CD=5.6cm$

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.