Question

Question #86513

Answer 1

As described below.

Explanation:

Given : `AB = BC = CD = DA = 5 cm` Also, `AC = 7 cm`

Since all the four sides are equal and diagonals bisect each other at right angles, it can be a rhombus or a square.

But `AB^2 + BC^2 != AC^2`. Hence it’s a `color(red)(Rhombus`.

Construction :

Draw a line AB of 5 cm.

With A as center,draw an arc of 7 cm radius. With B as center draw another arc of 5 cm radius. C is the the meeting point of the two arcs. Join AC & BC.

Now with A as center and radius of 5 cm, draw an arc. Likewise with C as center draw another arc of 5 cm. Intersecting point of the two arcs is D. Join AD , CD.

RHOMBUS ABCD is constructed.

You can verify, sides AB, CD are parallel; as also AD & BC.

Diagonals AC & BD bisect each other at right angles.