Q. 3 C5.0( 1 Vote )

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Answer :

We know that, area of a square with side √a will be a.

[Area of square = (side)^{2}]

Also, we can draw a square with area equal to a rectangle, we will use the area of rectangle in order to make the area equal to square.

side = √31 cm

Area of square = 31 cm^{2}

Area of rectangle = length × breadth = 31 cm^{2}

Here, let’s choose length = 6.2 cm and breadth = 5 cm

**Construction steps:**

1. Draw a rectangle ABCD with length, AB = 6.2 cm and breadth, BC = 5 cm.

2. Extend CD to CE, such that CE = BC = 5 cm.

3. Draw the perpendicular bisector of DE which bisects DE at O.

4. Taking O as center and OD = OE as radius, draw a semicircle.

5. Extend BC which intersects semicircle at F.

6. Draw a square CFGH taking CF as side.

Here,

Area of square CFGH = area of rectangle ABCD = 31 cm^{2}.

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<span lang="EN-USWest Bengal Board - Mathematics

<span lang="EN-USWest Bengal Board - Mathematics

<span lang="EN-USWest Bengal Board - Mathematics

<span lang="EN-USWest Bengal Board - Mathematics

<span lang="EN-USWest Bengal Board - Mathematics

<span lang="EN-USWest Bengal Board - Mathematics

<span lang="EN-USWest Bengal Board - Mathematics

<span lang="EN-USWest Bengal Board - Mathematics

<span lang="EN-USWest Bengal Board - Mathematics

<span lang="EN-USWest Bengal Board - Mathematics