Question

writing and solving equations practice (review)
name: krina patel period: 1st date: 9/22/25

1. write the equation using the perimeter. then, solve for z.
2. write the equation using the perimeter. then, solve for z.
3. the perimeter of a rectangle is 32 cm. the length is 1 cm more than twice the width. find the side lengths of the rectangle.
4. the perimeter of a rectangle is 35 cm. the length is 2.5 times the width. find the side lengths of the rectangle.

Explanation:

Step1: Recall perimeter formula

The perimeter of a polygon is the sum of the lengths of its sides.

Step2: Solve problem 1

For the first polygon with perimeter $P = 45$, the equation is $(z + 5)+z + 12+7 + 5+12=45$. Combining like - terms gives $2z+41 = 45$. Subtract 41 from both sides: $2z=45 - 41=4$, then $z = 2$.

Step3: Solve problem 2

For the second polygon with $P = 30$, the equation is $z+z+(z + 3)+2 + 4+(z + 3)=30$. Combining like - terms: $4z+12 = 30$. Subtract 12 from both sides: $4z=30 - 12 = 18$, then $z=\frac{18}{4}=\frac{9}{2}=4.5$.

Step4: Solve problem 3

Let the width of the rectangle be $w$. The length $l = 2w + 1$. The perimeter formula for a rectangle is $P=2(l + w)$. So $32=2((2w + 1)+w)$. Expand: $32=2(3w + 1)=6w+2$. Subtract 2 from both sides: $6w=32 - 2 = 30$. Divide by 6: $w = 5$. Then $l=2w + 1=2\times5+1 = 11$.

Step5: Solve problem 4

Let the width of the rectangle be $w$. The length $l = 2.5w$. Using the perimeter formula $P = 2(l + w)$, we have $35=2(2.5w+w)$. Combine like - terms inside the parentheses: $35=2(3.5w)=7w$. Divide both sides by 7: $w = 5$. Then $l=2.5w=2.5\times5 = 12.5$.

Answer:

1. $z = 2$
2. $z = 4.5$
3. Width $w = 5$ cm, Length $l = 11$ cm
4. Width $w = 5$ cm, Length $l = 12.5$ cm