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.

Answer 1

(a)

Steps for construction of rectangle:

1. Draw a straight line $AB$ of length $5cm$.

2. At both ends $A$ and $B$, draw perpendiculars on same side of $AB$.

3. Cut the arc of $4cm$ radius on both perpendiculars as $C$ and $D$

4. Join $CD$. $ABCD$ is the required rectangle.

Area of rectangle:

$Area\left(ABCD\right)=AB\times BC=5\times 4=20{cm}^2$

$Area\left(ABCD\right)=Area\left(PQRS\right)=20{cm}^2$

$PQRS$ is a square with side length $PQ$.

$\therefore ,PQ=2\sqrt{5}cm\approx 4.5cm$

Construction of Square:

1. Draw a straight line $PQ$ of length $\sim 4.5cm$.

2. At both ends $P$ and $Q$, draw perpendiculars on same side of $PQ$.

3. Cut the arc of $\sim 4.5cm$ 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 $10cm$ on this perpendicular bisector at $Z$

4. Join $XZ$ and $YZ$. $XYZ$ is the required isosceles triangle.