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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.

665148_628213_ans_ddef83d167824e2f940cb981b2eef83e.png

Maths

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