NCERT Solutions Ganita Prakash Chapter 8 & 196Section 8.3 Constructing Squares and Rectangles — In-text Questions
Book page 195 Updated on2026-09-05
Q1.
Now, let us start constructing squares and rectangles. How would you construct a square with a side of 6 cm?
Answer
Here is the full construction of the square PQRS of side 6 cm, exactly as in the six steps of the book.
Step 1. Draw a line segment PQ = 6 cm with a ruler.
Step 2. At P, draw a perpendicular to PQ. (Place the centre of the protractor on P, mark the 90° point, and join; or use the right-angled corner of a set square.)
Step 3. On this perpendicular mark S so that PS = 6 cm. Method 1: measure 6 cm with a ruler. Method 2: open the compass to 6 cm, put the tip at P and cut the perpendicular — the cut is S.
Step 4. At Q, draw a perpendicular to PQ in the same way.
Step 5. With the compass still open to 6 cm, put the tip at Q and cut this second perpendicular. Call the cut R.
Step 6. Join RS. PQRS is the required square.
The square PQRS of side 6 cm. The two grey arcs are the compass, opened to 6 cm, cutting the perpendiculars at S and at R.
Tip: the compass method (Method 2) is more accurate than measuring twice with a ruler, because the same opening is used for both sides — so PS and QR are certainly equal.
Q2.
Can you see why PS should be 6 cm long?
Answer
Yes — because of the very definition of a square.
Property S1: all the sides of a square are equal
PQ = 6 cm (already drawn)
so PS = QR = RS = 6 cm
Why it happens: PQ and PS are two sides of the same square meeting at the corner P. If PS were shorter or longer than PQ, the figure would still have four right angles but unequal sides — it would be a rectangle, not a square. Taking PS = 6 cm is what forces the figure to close as a square.
Q3.
How long is the side RS and what are the measures of ∠R and ∠S?
Answer
RS = 6 cm ∠R = 90° ∠S = 90°
Measure them in your figure — the ruler shows 6 cm and the protractor shows 90° at both corners.
Why it comes out this way without being asked for: we fixed PQ = 6 cm, made the two side lines perpendicular to PQ and cut off 6 cm on each. So S and R are both 6 cm above the base and the two perpendiculars are 6 cm apart — the segment RS joining them is therefore parallel to PQ, of the same length 6 cm, and it meets the two upright sides at right angles. The last two properties come free: you only need four correct steps to force a square.