Question

The difference between the adjacent sides of rectangle is 1 cm. Construct the rectangle ABCD if the perimeter is 14 cm. Find the measure the length of the diagonals.

• A. 8cm
• B. 6cm
• C. 5cm
• D. 4cm

Answer 1

The correct option is C 5cm

The difference between the adjacent sides of rectangle is 1 cm.

So, if length of the rectangle is $xcm$, then the breadth will be $(x-1)cm$

Perimeter of ABCD is 14 cm.
$\Rightarrow 2(x+(x-1\left)\right)=14$
$\Rightarrow 2x-1=\frac{14}{2}=7$
$\Rightarrow 2x=7+1=8$
$\Rightarrow x=\frac{8}{2}=4$
Thus, length = $4cm$ and breadth = $4-1=3cm$.

Steps of construction:

1. Draw a line segment AB of length $4cm$.
2. Construct right angles at A and B and extend the lines.
3. Keeping A and B as the centres, draw an arc of radius 3 cm on both the sides.
4. Mark them as D and C respectively. Join D and C
5. ABCD is the required quadrilateral.

Measure the length of AC and BD. It will be 5 cm in length.