A rectangular garden has length $2 x + 3$ m and breadth $3 x - 4$ m. If its perimeter is 48 m, find its area in square metres.

hard 4 marks Class 7 · Mathematics · Perimeter and Area

Answer

143 m²

The correct answer is 143 m² — Simplify inside brackets: $(2 x + 3) + (3 x - 4) = 5 x - 1$ . Equation becomes $2 (5 x - 1) = 48$ . Solve: $10 x - 2 = 48$ . Add 2 to both sides: $10 x = 50$ . Divide by 10: $x = 5$ . Find length: $2 x + 3 = 2 (5) + 3 = 13$ m. Find breadth: $3 x - 4 = 3 (5) - 4 = 11$ m. Area = length × breadth = $13 \times 11 = 143$ m².

Step-by-step solution

Perimeter of a rectangle = $2 (length + breadth)$ . Set up equation: $2 [(2 x + 3) + (3 x - 4)] = 48$ .
Simplify inside brackets: $(2 x + 3) + (3 x - 4) = 5 x - 1$ . Equation becomes $2 (5 x - 1) = 48$ . Solve: $10 x - 2 = 48$ . Add 2 to both sides: $10 x = 50$ . Divide by 10: $x = 5$ . Find length: $2 x + 3 = 2 (5) + 3 = 13$ m. Find breadth: $3 x - 4 = 3 (5) - 4 = 11$ m. Area = length × breadth = $13 \times 11 = 143$ m².

Common mistake: Misapplying the perimeter formula or arithmetic error in solving for

x

Concept tested: Using perimeter to find dimensions and area

Published 7 October 2026 · How this solution was prepared and checked

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A rectangular garden has length 2x+3 m and breadth 3x−4 m. If its perimeter is 48 m, find its area in square metres.

Step-by-step solution

A rectangular garden has length $2 x + 3$ m and breadth $3 x - 4$ m. If its perimeter is 48 m, find its area in square metres.