Construction of a Rectangle

Construction of a Rectangle

Let us now construct a rectangle with the given measurements

(i) length and breadth

(ii) a side and a diagonal

1. Construction of a rectangle when its length and breadth are given

Example 5.38

Construct a rectangle BEAN with BE = 5 cm and BN = 3 cm. Also find its area.

Solution:

Given: BE = 5 cm and BN = 3 cm

Steps:

1. Draw a line segment BE = 5 cm.

2. At B, construct BX ⊥ BE .

3. With B as centre, draw an arc of radius 3 cm and let it cut BX at N.

4. With E and N as centres, draw arcs of radii 3 cm and 5 cm respectively and let them cut at A.

5. Join EA and NA.

6. BEAN is the required rectangle.

Calculation of Area:

Area of rectangle BEAN = l × bsq.units

 = 5 × 3 =15 sq.cm

2. Construction of a rectangle when a side and a diagonal are given

Example 5.39

Construct a rectangle LIME with LI = 6 cm and IE = 7 cm. Also find its area.

Solution:

Given: LI = 6 cm and IE = 7 cm

Steps:

1. Draw a line segment LI = 6 cm.

2. At L, construct LX ⊥ LI .

3. With I as centre, draw an arc of radius 7 cm and let it cut LX at E.

4. With I as centre and LE as radius draw an arc. Also, with E as centre and LI as radius draw an another arc. Let them cut at M.

5. Join IM and EM.

6. LIME is the required rectangle.

Calculation of Area:

Area of rectangle LIME = l × b  sq.units

= 6 ×3.6 = 21.6 sq.cm