Question

helena builds a shed in her backyard. there are two sections, and each section has a square floor. what is the length of the entire shed? what subsets of the real numbers describe the length of the shed? the length of the entire shed is (type an exact answer, using radicals as needed.)

Explanation:

Step1: Find side - length of first square

For a square with area $A = 16\ ft^{2}$, using the formula $A = s^{2}$ (where $s$ is the side - length), we solve for $s$. So, $s_1=\sqrt{16}=4$ ft.

Step2: Find side - length of second square

For a square with area $A = 50\ ft^{2}$, using the formula $A = s^{2}$, we solve for $s$. So, $s_2=\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$ ft.

Step3: Calculate length of entire shed

The length of the entire shed is the sum of the side - lengths of the two squares. So, $L=s_1 + s_2=4 + 5\sqrt{2}$ ft.

Step4: Determine subset of real numbers

The length $4 + 5\sqrt{2}$ is an irrational number. Irrational numbers are a subset of real numbers. Also, since it represents a length, it is a positive real number.

Answer:

$4 + 5\sqrt{2}$ ft; The subset of real numbers is the set of positive irrational numbers.