  Question

(a) Draw a rectangle of sides $$5$$ centimetre and $$4$$ centimetre. Draw a square, equal in area to this rectangle.(b) Draw an isosceles triangle, equal in area to this square.

Solution

(a)Steps for construction of rectangle:1. Draw a straight line $$AB$$ of length $$5\ cm$$.2. At both ends $$A$$ and $$B$$, draw perpendiculars on same side of $$AB$$.3. Cut the arc of $$4\ cm$$ radius on both perpendiculars as $$C$$ and $$D$$4. Join $$CD$$. $$ABCD$$ is the required rectangle.Area of rectangle:$$Area(ABCD) = AB\times BC = 5\times 4 = 20\ {cm}^2$$$$Area(ABCD) = Area( PQRS) = 20 \ {cm}^2$$$$PQRS$$ is a square with side length $$PQ$$.$$\therefore, PQ = 2\sqrt5\ cm \approx 4.5\ cm$$Construction of Square:1. Draw a straight line $$PQ$$ of length $$\sim 4.5\ cm$$.2. At both ends $$P$$ and $$Q$$, draw perpendiculars on same side of $$PQ$$.3. Cut the arc of $$\sim4.5\ cm$$ radius on both perpendiculars as $$R$$ and $$S$$4. Join $$RS$$. $$PQRS$$ is the required square.(b)Construction of Triangle:1. Draw a line $$XY$$.2. Draw the perpendicular bisector of $$XY$$.3. Cut an arc of $$10 \ cm$$ on this perpendicular bisector at $$Z$$4. Join $$XZ$$ and $$YZ$$. $$XYZ$$ is the required isosceles triangle. Maths

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