Q. 45.0( 2 Votes )

Draw a square of area 5 square centimetres in three different ways.

Answer :

Way 1:


Steps of construction:


1. Draw a line BC = 5 cm, taking B and C as centres, draw


ABC = BCD = 90°, such that AB = CD = 1 cm



2. Join AD to get rectangle ABCD, here area(ABCD) = length × breadth = 5 × 1 = 5 cm.



3. From the rectangle drawn, extend AD by 3 cm to D'.



4. From the mid–point of AD'(Let it be O such that OA = OD'=4 cm) Draw a circle taking OA = OD' as radius.



3. Now, draw a chord PQ AD', passing through D.



6. Taking DP as side, draw a square DPRS, which is required.



Concept used:


The area of rectangle form of parts into which a diameter of a circle is cut by a perpendicular chord is equal to the area made by the square of half the chord.


And in the diagram, we made, AD' is diameter and PQ is perpendicular chord, therefore


Area(DPRS) = ar(ABCD) = 5 cm2


Way 2:


Steps of construction:


1) Make a line segment BC = 2 cm, and C draw AC BC such that AC = 1 cm



2) Join AB, here


AB = √(22 + 12) = √5 cm



3) At points A and B, draw perpendiculars AP AB and BQ AB, such that


AP = BQ = AB.



4) Join PQ, ABQP is required square and area(ABQP) = (√5)2 = 5 cm.



Way 3


1) Make a line segment BC = 3 cm, and C draw AC BC such that AC = 1 cm



2) Join AB, here


AB = √(32 + 12) = √10 cm



3) Draw the perpendicular bisector of AB, and name it as XY, XY intersects AB at O.



4) Taking O as centre, and OA = OB as radius, draw a circle which intersects XY at P and Q.



5) Join AP, PB, BQ and QA to get the required square.



Verification:


Here, AB = √10 cm is the diagonal of square, and we know, diagonal of a square of side a is equal to √2 a


2 a =10


a = 5 cm


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