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? a. whole numbers b. real numbers c. irrational numbers d. natural numbers e. integers f. rational numbers

Explanation:

Step1: Find side - length of first square

The area of the first square is $A_1 = 16\ ft^2$. Using the formula $A = s^2$ (where $s$ is the side - length of a square), we solve for $s_1$: $s_1=\sqrt{A_1}=\sqrt{16}=4$ ft.

Step2: Find side - length of second square

The area of the second square is $A_2 = 50\ ft^2$. Using the formula $A = s^2$, we solve for $s_2$: $s_2=\sqrt{A_2}=\sqrt{50}=5\sqrt{2}$ ft.

Step3: Calculate length of entire shed

The length of the entire shed $L=s_1 + s_2=4 + 5\sqrt{2}$ ft.

Step4: Determine subset of real numbers

Since $5\sqrt{2}$ is an irrational number and $4$ is a rational number, their sum $4 + 5\sqrt{2}$ is an irrational number. Irrational numbers are a subset of real numbers.

Answer:

The length of the entire shed is $(4 + 5\sqrt{2})$ ft.
B. Real numbers
C. Irrational numbers