Question

greg has 24 yard of material to make the fence around his new rectangular terrace. He plans to use all of the material
for his fence What should the length of the terrace be if it is 2yards greater than the width of terrace

Answer 1

Let the width of the terrace be \( w \) yards. Since the length is 2 yards greater than the width, we can express the length as \( l = w + 2 \) yards.

The perimeter \( P \) of a rectangle is given by the formula:

\[
P = 2l + 2w
\]

Greg has 24 yards of material for the fence, so:

\[
2l + 2w = 24
\]

We can simplify this equation:

\[
l + w = 12
\]

Now, substituting \( l \) with \( w + 2 \):

\[
(w + 2) + w = 12
\]

Combining like terms, we have:

\[
2w + 2 = 12
\]

Subtracting 2 from both sides:

\[
2w = 10
\]

Dividing by 2:

\[
w = 5
\]

Now, we can find the length \( l \):

\[
l = w + 2 = 5 + 2 = 7
\]

Thus, the dimensions of the terrace are:
- Width: 5 yards
- Length: 7 yards

Therefore, the length of the terrace should be **7 yards**.