Question

write the correct answer. 1. claire purchased just enough fencing to border either a rectangular or triangular garden, as shown, whose perimeters are the same. how many feet of fencing did she buy?

Explanation:

Step1: Calculate rectangle perimeter

The formula for the perimeter of a rectangle is $P = 2(l + w)$. Here, $l=3x - 3$ and $w=x - 3$. So $P_{rectangle}=2((3x - 3)+(x - 3))=2(4x-6)=8x - 12$.

Step2: Calculate triangle perimeter

The perimeter of a triangle is the sum of its side - lengths. So $P_{triangle}=(2x - 1)+(2x - 1)+2x=6x - 2$.

Step3: Set perimeters equal

Since the perimeters are the same, we set $8x - 12=6x - 2$.
Subtract $6x$ from both sides: $8x-6x - 12=6x-6x - 2$, which simplifies to $2x-12=-2$.
Add 12 to both sides: $2x-12 + 12=-2 + 12$, so $2x = 10$.
Divide both sides by 2: $x = 5$.

Step4: Find the perimeter

Substitute $x = 5$ into either the rectangle or triangle perimeter formula. Let's use the triangle formula $P=6x - 2$.
$P=6\times5-2=30 - 2=28$.

Answer:

28