A rectangular ground is marked by painting three of its sides. If the length…

Concept

In a rectangle, opposite sides are always equal in length, so the four sides form two pairs of equal sides — a length pair and a breadth pair. The perimeter is the sum of all four sides, that is 2 × (length + breadth).

Working

1. Let the unpainted side have length 13 m.

2. Because opposite sides of a rectangle are equal, the side directly opposite the unpainted one is also 13 m long — and since exactly one side is unpainted, that opposite side is one of the three painted sides.

3. So the three painted sides consist of one side of length 13 m (equal to the unpainted side) plus both sides of the other pair, each of some length y.

4. Sum of the painted sides: 13 + 2y = 57.

5. Solve for y: 2y = 57 − 13 = 44, so y = 22 m.

6. Area of the rectangle = 13 m × 22 m = 286 m².

Check

Check using the total perimeter: 2 × (13 + 22) = 70 m. The painted sides (57 m) plus the unpainted side (13 m) also add to 70 m, confirming that the side lengths 13 m and 22 m are consistent.

So the area of the ground is 286 m².