Question

Sophia wanted to increase the area of her vegetable garden she extended the length from 10 feet to 30 feet how many times larger is the are of the garden

Answer 1

The new area of garden is 3 times of the initial area of the garden.

Explanation:

The initial length of the garden is 10 feet.

The shape of the garden must be a rectangle and the area of rectangle is

`A=l* w`

The initial area of the garden is

`A_0=10* w`

`A_0=10w`

The new length of the garden is 30 feet. So, the new area of the garden is

`A_1=30* w`

`A_1=30w`

Let area of garden is k times larger than the initial area.

`A_1=k* A_0`

`30w=k* 10w`

Divide both sides by 10w.

`k=3`

Therefore new area of garden is 3 times of the initial area of the garden.