Question

the graph below shows the relationship between the perimeter of a square and the length of a side of the square. perimeter and side length. which proportion could be used to find s, the length of the side of a square with a perimeter of 70 inches?

Explanation:

Step1: Recall perimeter formula for square

The perimeter $P$ of a square is given by $P = 4s$, where $s$ is the side - length of the square. We can set up a proportion using the relationship between perimeter and side - length. If we consider two pairs of perimeter and side - length values, say $(P_1,s_1)$ and $(P_2,s_2)$, the proportion is $\frac{P_1}{s_1}=\frac{P_2}{s_2}$. We know that for a square, the ratio of perimeter to side - length is always 4. Let $P_1 = 4$, $s_1 = 1$ (a square with side - length 1 has perimeter 4) and $P_2=70$, $s_2 = s$ (the side - length we want to find). So the proportion is $\frac{4}{1}=\frac{70}{s}$.

Step2: Cross - multiply the proportion

Cross - multiplying the proportion $\frac{4}{1}=\frac{70}{s}$ gives us $4s=70$.

Step3: Solve for $s$

Dividing both sides of the equation $4s = 70$ by 4, we get $s=\frac{70}{4}$.

Answer:

The proportion $\frac{4}{1}=\frac{70}{s}$ (equivalent to $\frac{s}{1}=\frac{70}{4}$) can be used to find $s$. Among the options (not shown completely in the question but based on the correct proportion concept), the correct proportion is one that represents the ratio of perimeter to side - length of a square as 4. If the options are in the form of $\frac{\text{perimeter}}{\text{side - length}}$ ratios, the correct one is $\frac{70}{s}=\frac{4}{1}$ or $\frac{s}{1}=\frac{70}{4}$.