Question

If the perimeter of a garden of area 800 m$^2$ is 120 m and its length is twice the breadth, then find its length and breadth.

Hint:

For rectangle problems, always form two equations — one from perimeter and one from area — to find unknown dimensions.

Answer 1

Step 1: Let the breadth be \(x\) m. 
Then, the length = \(2x\) m (given). 
Step 2: Write the formula for perimeter. 
\[ \text{Perimeter} = 2(l + b) \] Substitute: \[ 120 = 2(2x + x) \Rightarrow 120 = 6x \Rightarrow x = 20 \] Step 3: Find the length. 
\[ l = 2x = 2 \times 20 = 40 \] Step 4: Verify using the area condition. 
\[ \text{Area} = l \times b = 40 \times 20 = 800 \, \text{m}^2 \] The condition is satisfied. 
Step 5: Conclusion. 
Hence, the length = 40 m and breadth = 20 m.