Answer:
Length = 34 and Width = 30
Step-by-step explanation:
This is a simple system of equation that is mainly solved using substitution, so keep in mind the following key points:
- Rectangle's Perimeter is 128 ft.
- "the garden is 4 feet longer than it is wide," this simply means that the Length is 4 feet longer than the Width: which algebraically translates to [tex]L = 4 + W[/tex]
- Perimeter formula for Rectangle is [tex]P = 2(L+W)[/tex]
First, we find the Width by plugging the given values in the formula:
[tex]128 = 2((4 + W) + W)\\128 = 8 +2W + 2W\\120 = 2W + 2W\\120 = 4W\\W = \frac{120}{4}\\\ W = 30[/tex]
All we did here was substituting 4 + W for L to find the Width.
Now, to find the Length we plug in the value of W and solve for L:
[tex]128 = 2(L + 30)\\\frac{128}{2} = (L + 30)\\64 = L + 30\\64 - 30 = L\\L = 34[/tex]
Tip: always sketch a rough geometrical diagram of word problems, it helps. (Refer to the diagram attached)
Keep working hard and good luck. <3
