Question

geometry ic sem b
classifying quadrilaterals
the perimeter of the rectangle is 28 units.
what is the value of w?
5 units
15 units
14 units
the perimeter of the rectangle is 28 units.
w
2w - 1

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2(l + w)$, where $P$ is the perimeter, $l$ is the length and $w$ is the width. Here, $P = 28$, $l=2w - 1$ and width is $w$. So, $28=2((2w - 1)+w)$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $(2w - 1)+w=3w - 1$. Then the equation becomes $28 = 2(3w - 1)$. Distribute the 2 on the right - hand side: $28=6w-2$.

Step3: Solve for $w$

Add 2 to both sides of the equation: $28 + 2=6w-2 + 2$, which gives $30 = 6w$. Divide both sides by 6: $\frac{30}{6}=w$, so $w = 5$.

Answer:

5 units