Draw a rectangle of one side 6 centimetres and area equal to that of a square of side 5 centimetres.

1. Draw a circle of any radius with center as O, take any point A on its circumference and Join OA.

2. Draw AX perpendicular to OA, such that AX is tangent to circle.

3. Draw an arc of radius 5 cm taking A as center which intersects AX at B and the draw and arc of radius 4 cm taking B as center which intersects circle at C.

4. Join BC and extend it to D, such that point D lies on the circle.

5. Draw BY ⊥ BD and taking B as center and BD as radius draw an arc which intersect BY at E

6. Taking BC as breadth and BE as length draw a rectangle BCFE, which is required rectangle.

Verification of area:

We know that,

The rectangle with the intersecting line and its part outside the circle as sides and square with tangent as side have equal area.

i.e. area of rectangle with sides as BD and BC = area of square of side AB

now,

AB = 5 cm, By construction and BC = 4 cm By construction

Also, BD = BE

So, area of rectangle having sides as 4 cm and BE = area of square of side as 5 cm.