Question

Draw a rectangle of width 5 centimetres and height 3 centimetres. 

i. Draw a rectangle of the same area with width 6 centimetres. 

ii. Draw a square of the same area.

Answer 1

i. Draw a rectangle of length 5 cm and width 3cm.

Extend AB up to 6cm. 

(AE = 6cm) Draw an arc having radius as AE and A as centre. Extend DA and mark the point F.

Extend BA towards left. Mark G as AD = AG 

Draw Δ GFB.

Circum circle of Δ GFB meets AD at D. 

∴ AG × AB = AF × AH. 

That is area of the rectangle having length 

AB and width AD is equal to the area of

rectangle having length AE and width AH.

ii. Draw a rectangle of length 5cm and width 3cm. Area = 5 x 3 = 15 cm². 

Therefore side of a square will be √15.

Draw a semicircle of diameter AH. 

Extend BC, and mark the point F. 

AB × BH = 5 × 3 = 15 

AB × BH = BF² ; BF = √5 cm 

Area of BEGF = √15 × √15 = 15 cm²