Page 231 - Ganit Kaushal

3. When a Diagonal and a Side are Given

A B
Construction 8: Construct a rectangle where one of its sides is 5 cm and the length of a Rough
diagonal is 7 cm. (NCERT) diagram 7 cm
Sol. Let us first draw a rough diagram as given in the adjoining figure. It will help us in
deciding the steps of construction, i.e., which line to draw first. D 5 cm C
Follow the steps given: D 5 cm C

Step 1: Draw the baseline DC of length 5 cm using a ruler and a pencil (see figure (i)). (i)
Step 2: Now, draw a perpendicular to the line DC at point C
with the help of a protractor as explained in construction 5 (see B
figure (ii)).
Step 3: We know that point B is at a distance of 7 cm from point 7 cm
D. Now, using a ruler, take the distance of 7 cm on a compass,
and from D, mark an arc cutting the perpendicular line at B. D 5 cm C D 5 cm C
Join BD (see figure (iii)). (ii) (iii)
A B
Step 4: Now, construct perpendiculars to DC and BC at points D and B, respectively, 90°
with the help of a protractor. The point where these perpendiculars intersect is the
fourth point A.
We get the required rectangle ABCD as shown in the adjoining figure (iv). 90°
D C
Check if ABCD is indeed a rectangle satisfying properties R1 and R2. (iv)
4. When a Rectangle is Divided into Three Squares

Construction 9: Construct a rectangle that can be divided into three identical A P Q B
squares. (NCERT) Rough
Sol. First we will draw a rough diagram of a rectangle divided into three diagram
identical squares. Now, to construct a rectangle that can be divided D S R C
into three identical squares, we need to start by selecting the shorter side of any length. Then the longer
side must be chosen so that its length is exactly thrice that of A A
the shorter side.
Follow the steps given below:
Step 1: Draw the line AD of any length with the help of a ruler
and pencil. (See figure (i)) D D
(i) (ii)
Step 2: Using a protractor, draw a perpendicular to line
AD at point A long enough to contain thrice the length
of AD. (See figure (ii))

Step 3: Set your compass to the length AD (See figure
(iii)). Now, without changing the setting of the compass, A P Q B
put the pointer at A and draw an arc to cut it at P.
Now, put the pointer at P and draw an arc cutting the
perpendicular at Q. Then put the pointer at Q and draw
an arc to cut the perpendicular at B. (See figure (iii)) D (iii)

Playing with Constructions 229