Construct a Rhombus WXYZ such that WX = 6 cm and Angle X = 105°
(Use compass to make 105°)
Answers
. A rhombus whose diagonals are 5.2 cm and 6.4 cm long.
Sol. Let diagonal AC = 5.2 cm and diagonal BD = 6.4 cm
Draw AC = 5.2 cm. Draw XY, the perpendicular bisector of AC which cuts AC at O.
With O a centre, draw arcs of radii
which cut OX at D and OY at B.
Join AB, BC, CD and DA.
Then, ABCD is the required rhombus.
3. A rectangle with adjacent sides of lengths 5 cm and 4 cm.
Sol. In a rectangle, opposite sides are equal and each of 4 angles is equal to 90°.
Let AB = DC = 5 and BC = 4 cm
∴AB = DC = 5 cm and BC = AD = 4 cm.
Also, ∠A = ∠B = ∠C = ∠D = 90°.
Steps of construction
1. Draw AB = 5 cm.
2. Draw ∠ABX = 90°.
3. Cut off BC = 4 cm on BX.
4. With A as centre and radius equal to 4 cm, cut off an arc.
5. With C as centre and radius equal to 5 cm cut off another arc on the arc drawn in step-4 at point D.
6. Join AD and CD.
Hence, ABCD is the required