Question

Construct a quadrilateral ABCD in which AB = CD = 3 cm, BC = AD = 4 cm and
diagonals are 5 cm each. What type of quadrilateral is it?
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Answer 1

Answer:

First we draw a rough sketch of a quadrilateral ABCD and write down its dimensions as shown. We may divide it into two conveniently constructible Δs ABC and ACD.

Steps of construction:

1. Draw AC = 7 cm.

2. With A as centre and radius 4.5 cm, draw an arc (below AC).

3. With C as centre and radius 5.5 cm, draw another arc cutting the previous arc at B.

4. Join AB and BC

5. With A as centre and radius 6 cm, draw an arc (above AC).

6. With C as centre and radius 4 cm, draw another arc cutting the previous arc and D.

7. Join AD = CD.

Then, ABCD is the required quadrilateral.

(ii) First we draw a rough sketch of a quadrilateral JUMP and write down its dimensions as shown.

We may divide it inot two conveniently constructible Δs PJU and PMU.

Steps of construction:

1. Draw PU = 6.5 cm

2. With P as centre and radius 4.5 cm, draw an arc(below (PU)

3. With U as centre and radius 3.5 cm, draw another arc cutting the previous arc at J.

4. Join PJ and JU.

5. With P as centre and radius 5 cm, draw an arc (abov PU).

6. With U as centre and radius 4 cm, draw another arc cutting the previous arc at M.

7. Join PM and UM.

Then, JUMP is the required quadrilateral.

(iii) We know that opposite sides of parallelogram are equal and parallel to each other.

∴ OR = ME and MO = ER.

Steps of Construction:

1. Draw OR = 5 cm

2. With R as centre and radius equal to 4.5 cm, cut an arc.

3. With O as centre and radius equal to 7.5 cm, cut another arc on the arc drawn in step-2 at point E.

4. With E as centre and radius equal to 6 cm, cut an arc.

5. With O as centre and radius equal to 4.5 cm, cut an arc on the arc drawn in step-4 at point M.

6. Join RE, OE, OM and ME.

Hence, MORE is the required parallelogram.

(iv) We know that all four sides of a rhombus are equal.

∴ BE = ES = ST = BT = 4.5 cm.

Steps of Construction:

1. Draw BE = 4.5 cm.

2. With B as centre and radius equal to 4.5 cm, draw an arc.

3. With E as centre and radius equal to 6 cm, draw another arc, cutting the previous arc at point T.

4. With E as centre and radius equal to 4.5 cm, cut an arc.

5. With T as centre and radius equal to 4.5 cm, cut another arc on the previous arc at point S.

6. Join BT, ES, ET and ST.

Hence, BEST is the required rhombus.