November 2022

Isabella created a tomato garden, but now she’s decided that she wants to expand it. The tomato plants were arranged in the shape of a square. Isabella wants to add both an extra row and an extra column to form a new square. To do this, she had to be 21 more tomato plants to fill in the new spaces. How many tomato plants will be in the new garden?


In situations like this, it is usually helpful to use a smaller example. If Isabella started with a 3x3 grid of tomato plants (green) and wanted to add more to make a 4x4 grid of tomato plants (blue), she would need seven new plants. This is because you would have twice the side length of the square (light blue) and one more to be placed in the corner (dark blue). In this case that would be (2 x 3) + 1 = 7

For the garden asked about in the question, she needs 21 plants to increase the side lengths by one. By representing the length of the sides of the initial garden by s:
2s + 1 = 21
2s = 20
s = 10

Therefore before she expanded it, Isabella had a garden of 10 plants by 10 plants. When she expands it, she'll have a garden of 11 plants by 11 plants. This will mean she will have 11 x 11 = 121 tomato plants in her new garden.