Question

construct a rhombus pqrs whose diagonals PR and QS are 8 cm and 6 CM respectively find by construction a point X equidistant from PQ, PS and EQ distance from R ,S .Measure XR
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Answer 1

Given:

A rhombus PQRS whose diagonals PR and QS are 8cm and 6cm, respectively.

To find:

The construction of the rhombus PQRS.

Solution:

A rhombus is a special type of parallelogram whose each side is of equal length and the diagonals bisect each other at right angles.

To construct a rhombus PQRS with diagonals PR = 8cm and QS = 6cm, the following steps can be used.

Step 1. First, draw PR = 8 cm.

Step 2. Draw a perpendicular bisector of diagonal PR that meets PR at O.

Step 3. Taking O as the centre, draw an arc OQ = OS = 5 cm which intersects the perpendicular bisector.

Step 4. Join PQ, QR, RS and PS.

Hence, the required rhombus PQRS is constructed.

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