Page 232 - Ganit Kaushal

Step 4: Now draw a perpendicular to line AD at point D. Divide A P Q B
this perpendicular into three equal parts just as done from point A,
to mark points S, R, and C. Each part is equal to AD.

Step 5: Join the points P and S, Q and R, B and C, respectively.
D S R C
We get the required rectangle ABCD that is divided by identical (iv)
squares into three parts as given in the adjoining figure (iv).

5. When a Square is in the Centre of a Rectangle

Construction 10: Construct a rectangle of sides 8 cm and 4 cm. Construct a square 8 cm
inside, as shown in the figure, such that the centre of the square is the same as the
centre of the rectangle. (NCERT) 4 cm

Sol. To construct the given figure, follow the steps given below:
Step 1: Draw line AB of length 4 cm using a ruler and pencil (see A A 8 cm D
figure (i)).

Step 2: Draw perpendiculars to the line AB at B and A, respectively, 4 cm 4 cm
using a protractor. With the help of a ruler, make sure that the length B B C
of each perpendicular is 8 cm. Mark the other endpoints of these lines (i) (ii)
as C and D, respectively (see adjoining figure (ii)).
Step 3: To construct the square, set the compass to 2 cm. A 2 cm P Q 2 cm D
From A, draw an arc on AD to mark point P. From D, draw

an arc on AD to mark Q. Similarly, from B draw an arc on 4 cm
BC to mark point S and from C mark point R (see B S R C
figure (iii)). (iii)
Step 4: Join the points P to S, Q to R and D to C respectively to get the 2 cm P Q 2 cm
required rectangle ABCD (see figure (iv)). PQRS is the required square inside A D
the rectangle ABCD. After completing the construction, readers are expected 4 cm
to measure the sides and angles of PQRS and figure out if it satisfies the B C

rules S1 and S2 or not. This will confirm if PQRS is a square or not. S R
(iv)
Exercise 8.2

1. Draw a square with a side length of 5.5 centimetres.
2. Draw a rectangle of sides 5 cm and 10 cm. After drawing, check if it satisfies both the properties R1
and R2 of the rectangle.

3. Draw a rectangle with sides of length 8 cm and 6 cm. What is the length of the largest line that can
be drawn inside this rectangle?
4. Construct a rectangle in which one of the diagonals divides the opposite angles into 55° and 35°.
5. Construct a rectangle that can be divided into two identical squares. (Hint: see construction-9)

(NCERT)

230 Mathematics-6