NCERT Solutions Exploring Society: India and Beyond Chapter 1 Scale — Let's Explore
Book page 10 Updated on2026-09-05
Q1.
Draw a simple map of a school's playground. Let us assume it is a rectangle, 40 m in length and 30 m in width. Draw it precisely with your ruler on a scale of 1 cm = 10 m.
Answer
Convert each real measurement into centimetres on the paper using the given scale.
Scale: 1 cm on the map = 10 m on the ground
Length 40 m → 40 ÷ 10 = 4 cm
Width 30 m → 30 ÷ 10 = 3 cm
So draw a rectangle of 4 cm × 3 cm with your ruler.
The playground drawn to scale: every 1 cm of the drawing stands for 10 m of real ground.
Why the shape stays correct: both sides are divided by the same number, so the drawing has the same shape as the real playground, only smaller. If you shrank the length but not the width, the map would lie about the ground.
Q2.
Now measure the diagonal of the rectangle. How many centimetres do you get? Using the scale, calculate the real length of the playground's diagonal, in metres.
Answer
Put your ruler from one corner to the opposite corner of the 4 cm × 3 cm rectangle.
Measured diagonal on the map = 5 cm
1 cm stands for 10 m
Real diagonal = 5 × 10 = 50 metres
Check it without the ruler. The sides 30 m, 40 m and the diagonal form a right-angled triangle:
40² + 30² = 1600 + 900 = 2500
√2500 = 50 m ✔
Why the two answers agree: a map drawn to scale is a faithful small copy of the ground. Anything you measure on it — a side, a diagonal, the distance between two trees — can be turned back into a real distance by multiplying by the scale. This is exactly what you will do in the exercise with the Narmada and the Ganga.
Did you know? 3, 4, 5 is the most famous right-angled triple. Masons in India still use a knotted 12-unit string (3 + 4 + 5) to set out a perfect right angle for the corner of a house.