The correct option is A
- Perimeter of ABCD = 18 cm... (i)
- Opposite sides are equal and parallel...(ii)
- Adjacent sides are 1 cm more than the other...(iii)
- One angle measure 60°...(iv)
Let us consider a rough sketch of ABCD.
AB and BC are adjacent sides and measure of AB = x, the measure of CD = x + 1.
From (i), (ii) and (iii),
AB + BC + CD + DA = 18cm
x + x + 1 + x + x + 1 = 18 cm ⇒
4x + 2 = 18 cm ⇒
4x = 16 cm ⇒
x = 164
= 4 cm.
Then, AB = 4 cm, CD = 4 + 1 = 5 cm.
Now, CD = 4 cm and BC = 5 cm.
From (ii), ABCD is a parallelogram.
Hence, AB || CD. ∠DAB+∠ADC=180°
(Co-interior angles are supplementary) ⇒60°+∠ADC=180° ⇒∠ADC=120°
Steps of construction:
Step 1: Draw a line segment AB of length 4 cm
Step 2: Construct an angle of 60° at the point A and extend the line.
Step 3: Keeping A as the centre, draw an arc of radius 5 cm on the extended line and mark it as D.
Step 4: Construct 120° at D and extend the line.
Step 5: Keeping D as the centre, draw an arc of radius 4 cm on the extended line and mark it as C.
Step 6: Join B and C.
After construction, we get the following quadrilateral.