A rectangular field measures 68.5 m by 45.6 m. A path of uniform width 2.4 m is constructed around the outside of the field. Find the difference between the outer perimeter of the path and the perimeter of the original field.
19.2 m
The field is a rectangle of length 68.5 m and breadth 45.6 m. A path of uniform width 2.4 m runs all around the outside of the field, so the outer boundary of the path is itself a larger rectangle, concentric with the field.
Step 1 — Perimeter of the original field.
Perimeter = 2 × (length + breadth) = 2 × (68.5 + 45.6) = 2 × 114.1 = 228.2 m.
Step 2 — Outer dimensions of the path. Because the path is added on both sides of each dimension, each side grows by 2 × 2.4 = 4.8 m:
- Outer length = 68.5 + 4.8 = 73.3 m
- Outer breadth = 45.6 + 4.8 = 50.4 m
Step 3 — Outer perimeter.
= 2 × (73.3 + 50.4) = 2 × 123.7 = 247.4 m.
Step 4 — Difference.
247.4 − 228.2 = 19.2 m.
A useful shortcut: for any rectangle, adding a uniform border of width w all around increases the perimeter by exactly 8w, no matter what the original length and breadth are. Here 8 × 2.4 = 19.2 m, which matches instantly. This is because each of the four corners contributes an extra 2w to the boundary path. Notice the answer does not depend on the numbers 68.5 or 45.6 at all.
The values 17 m, 20 m and 18.5 m do not correspond to 8 × 2.4; they would arise only from arithmetic slips such as adding the width on one side only (which would give 4w) or mis-computing the increment. The correct difference is 19.2 m.
Similar Questions
- A circle, made of wire, of diameter 49 cm is formed into a rectangle whose sides are in the ratio 7 : 4. Find the area of the rectangle. [Take $\pi = \frac{22}{7}$]
- What is the area of the region swept by the minute hand $6\text{ cm}$ long, of a wall clock, in an interval of 5 minutes?
- The area of a rectangle with a length of 121 m is the same as that of a square with a side of 44 m. Find the width of the rectangle.
- Find the cost of carpeting a 15-m-long and 11-m-wide room with a 75-cm-wide carpet, if the price of the carpet is ₹13 per meter (not considering the cost of labour).
Important Questions from Mensuration
A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?
A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A?
A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden
A village having a population of 4000 requires 150 liters of water per head per day. It has a tank measuring 20 m x 15 m x 6 m. The water of this tank will last for
The centroid of an equilateral triangle ABC is G. If AB is 6 cms, the length of AG is
