Question

Using ruler and compasses only, construct a rhombus whose diagonals are 8 em and 6 cm. Measure the length of its one side.

Answer 1

A rhombus has diagonals perpendicular to each other.
1. Draw $AC=6cm$
2. Draw perpendicular bisector XY of AC intersecting AC at O.
3. Taking O as centre and $\frac{1}{2}\times 8=4cm$ as radius draw two arcs intersecting OX and OY at B and D respectively.
4. Join AB, BC, CD and AD.
ABCD is the required rhombus with side $5cm.$