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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.

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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×BC=5×4=20 cm2

Area(ABCD)=Area(PQRS)=20 cm2
PQRS is a square with side length PQ.
,PQ=25 cm4.5 cm

Construction of Square:
1. Draw a straight line PQ of length 4.5 cm.
2. At both ends P and Q, draw perpendiculars on same side of PQ.
3. Cut the arc of 4.5 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

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