question_answer 5)

                Draw the following: 1. The square READ with RE = 5.1 cm. 2. A rhombus where diagonals are 5.2 cm and 6.4 cm long. 3. A rectangle with adjacent sides of lengths 5 cm and 4 cm. 4. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm.

Answer:

                1. Steps of Construction 1. Draw RE =5.1 cm. 2. At R, draw a ray RX such that \[\angle ERX={{90}^{\text{o}}}\].   3. From ray RX, cut RD = 5.1 cm.   4. At E, draw a ray EY such that \[\angle REY={{90}^{\text{o}}}\].                                  5. From ray EY, cut EA = 5.1 cm.   6. Join AD.                      Then, READ is the required square.                 2. Steps of Construction    1. Draw AC = 5.2 cm.              2. Construct its perpendicular bisector Let them meet at O.        3. Cut off \[\frac{6.4}{2}=3.2\,cm\] lengths on either side of the drawn bisector, we get B and D. 4. Join AB, BC, CD and DA. Then, ABCD is the required rhombus.                 3. Steps of Construction 1. Draw PQ = 5 cm. 2. At Q, draw a ray QX such that \[\angle PQX={{90}^{\text{o}}}\]. 3. From ray QX, cut QR = 4 cm. 4. Through P, draw a ray PY parallel to QR. 5. Through R, draw a ray RZ parallel to QP to meet the ray of step 4 at S. Then, PQRS is the required rectangle.                 4. Steps of Construction 1. Draw OK = 5.5 cm. 2. At K, draw a ray KX. 3. From ray KX, cut KA = 4.2 cm. 4. Through A, draw a ray AT parallel to KO. 5. Through O, draw a ray OZ parallel to KA to cut the ray of step 4 at Y. Then, OKAY is the required parallelogram.