  Question

# The total perimeter of a quadrilateral ABCD is 18 cm. The opposite sides are equal and parallel. The adjacent sides are 1 cm more than the other. One of the angles of the quadrilateral ABCD measures 60°. Construct the quadrilateral ABCD.    Solution

## The correct option is A Given, 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.   Suggest corrections   