Question

1. a square garden has an area of 137 square feet. what is the approximate length of one side of the garden?

Explanation:

Step1: Recall the formula for the area of a square

The area \( A \) of a square is given by the formula \( A = s^2 \), where \( s \) is the length of a side. So, to find the side length, we need to solve for \( s \), which gives \( s=\sqrt{A} \).

Step2: Substitute the given area into the formula

We know that the area \( A = 137 \) square feet. So we need to calculate \( s=\sqrt{137} \).
We know that \( 11^2 = 121 \) and \( 12^2=144 \). Since \( 121<137 < 144 \), \( \sqrt{121}<\sqrt{137}<\sqrt{144} \), so \( 11 < \sqrt{137}<12 \).
Now, let's calculate a more approximate value. \( 11.7^2=136.89 \) and \( 11.8^2 = 139.24 \). Since \( 136.89\approx137 \), we can say that \( \sqrt{137}\approx11.7 \) (because \( 11.7^2 = 136.89\) which is very close to 137).

Answer:

The approximate length of one side of the garden is about \( 11.7 \) feet (or we can also say approximately 12 feet as a rougher approximation, but \( 11.7 \) is more accurate). If we consider the value from the square root calculation, \( \sqrt{137}\approx11.7 \) feet.