question_answer 2)

                Construct the following quadrilaterals: (i) Quadrilateral LIFT LI = 4 cm IF = 3 cm TL = 2.5 cm LF = 4.5 cm IT = 4 cm (ii) Quadrilateral GOLD OL = 7.5 cm GL = 6 cm GD = 6 cm LD = 5 cm OD = 10 cm (iii) Rhombus BEND BN = 5.6 cm DE = 6.5 cm

Answer:

                (i) Steps of Construction 1. Draw LI = 4 cm. 2. With L as centre and radius LT = 2.5 cm, draw an arc. 3. With I as centre and radius IT = 4 cm, draw another arc to intersect the arc of step 2 at T. 4. With I as centre and radius IF = 3 cm, draw an arc. 5. With L as centre and radius LF = 4.5 cm, draw another arc to intersect the arc of step 4 at F. 6. Join IF, FT, TL, LF and IT. Then, LIFT is the required quadrilateral. (ii) Steps of Construction 1. Draw LD = 5 cm. 2. With L as centre and radius LG = 6 cm, draw an arc. 3. With D as centre and radius DG = 6 cm, draw another arc to intersect the arc of step 2 at G. 4. With L as centre and radius LO = 7.5 cm, draw an arc. 5. With D as centre and radius DO = 10 cm, draw another arc to intersect the arc of step 4 at O. 6. Join DG, GO, OL, LG and DO. Then GOLD is the required quadrilateral. (iii) Steps of Construction 1. Draw DE = 6.5 cm. 2. Draw perpendicular bisector PQ of DE. Let M be the mid-point of DE. 3. Cut \[MN=\frac{1}{2}\times 5.6\,cm\,=2.8\,cm\] from MP. 4. Cut \[MB=\frac{1}{2}\times 5.6\,cm\,=2.8\,cm\] from MQ. 5. Join DN, NE, EB and BD. Then, BEND is the required rhombus.