1. Mr. Tsilatsila builds a fence around his rectangular vegetable garden of \( 8 \mathrm{~m}^{2} \). If the length is twice the breadth, determine the dimensions of Mr. Tsilatsila's vegetable garden.

To find the dimensions of Mr. Tsilatsila's vegetable garden, we can set up the problem using algebra. Let the breadth be \( b \) meters. Since the length is twice the breadth, we can express the length as \( 2b \). The area \( A \) of the rectangle can be written as: \[ A = \text{length} \times \text{breadth} = 2b \times b = 2b^2 \] We know the area is \( 8 \, \mathrm{m}^{2} \): \[ 2b^2 = 8 \] Dividing both sides by 2 gives us: \[ b^2 = 4 \] Taking the square root of both sides, we find: \[ b = 2 \, \mathrm{m} \quad \text{(breadth)} \] Now, substituting back to find the length: \[ \text{length} = 2b = 2 \times 2 = 4 \, \mathrm{m} \] Thus, the dimensions of Mr. Tsilatsila's vegetable garden are a breadth of \( 2 \, \mathrm{m} \) and a length of \( 4 \, \mathrm{m} \). Now he can grow those delicious veggies happily! 🌱🥕