Question

18 trudi wants to put a fence around her garden. she has 32 yards of fence material. does she have enough to go all the way around the garden? explain why or why not. trudis garden 6\frac{3}{4} yards 8\frac{1}{2} yards

Explanation:

Step1: Identify the shape and dimensions

The garden appears to be a rectangle with length \( l = 8\frac{1}{2} \) yards (which is \( \frac{17}{2} \) yards) and width \( w = 6\frac{3}{4} \) yards (which is \( \frac{27}{4} \) yards).

Step2: Calculate the perimeter of a rectangle

The formula for the perimeter \( P \) of a rectangle is \( P = 2(l + w) \).

First, find \( l + w \):
\( l + w=\frac{17}{2}+\frac{27}{4}=\frac{34 + 27}{4}=\frac{61}{4} \) yards.

Then, find the perimeter:
\( P = 2\times\frac{61}{4}=\frac{61}{2}=30.5 \) yards.

Step3: Compare the perimeter with the available fence material

Trudi has 32 yards of fence material. Since \( 30.5<32 \).

Answer:

Yes, Trudi has enough fence material. The perimeter of the garden is \( 30.5 \) yards (or \( 30\frac{1}{2} \) yards) and she has 32 yards of fence material, and \( 30.5<32 \), so the 32 - yard fence material is sufficient to go around the garden.