Question

to solve the problem. mr. jiang is building a deck on his house. he can calculate the perimeter of the deck using this formula: p = 4s 9) solve the equation to show the length of a side—that is, solve for s. 10) is mr. jiang’s deck in the shape of a square or a rectangle? explain your answer.

Explanation:

Question 9

Step1: Start with the formula \( P = 4s \)

We have the equation \( P = 4s \) and we need to solve for \( s \).

Step2: Divide both sides by 4

To isolate \( s \), we divide each side of the equation by 4. Using the division property of equality, if \( P = 4s \), then dividing both sides by 4 gives \( \frac{P}{4}=\frac{4s}{4} \).

Step3: Simplify the right - hand side

Simplifying \( \frac{4s}{4} \) gives \( s \). So we have \( s=\frac{P}{4} \).

The formula for the perimeter of a square is \( P = 4s \), where \( s \) is the length of a side (all sides of a square are equal). The formula for the perimeter of a rectangle is \( P=2(l + w) \), where \( l \) is the length and \( w \) is the width (and \( l
eq w \) in general for a non - square rectangle). Since Mr. Jiang used the formula \( P = 4s \) to calculate the perimeter of his deck, this formula is characteristic of a square (where all four sides are equal in length). So the deck is in the shape of a square.

Answer:

\( s = \frac{P}{4} \)

Question 10