find the dimensions of a rectangular garden with an 32 square meters and a perimeter of 24 meters. show your process
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find the dimensions of a rectangular garden with an 32 square meters and a perimeter of 24 meters. show your process
Answer:
Length = 8 meters
Width = 4 meters
Step-by-step explanation:
Given:
Area = 32 m²
Perimeter = 24
Formulas:
Area = LW
Perimeter = 2L + 2W
Solution:
Step 1: Equate the given to their respective formula.
LW = 32
2L + 2W = 24
Step 2: Find the representation of one of the variables of either of the two equations.
In this case, I'll find the representation of W of the second equation.
2L + 2W = 24
↓
L + W = 12
↓
W = 12 - L
Step 3: Substitute it to the other equation to find the value of the other variable.
LW = 32
↓
L(12 - L) = 32
↓
12L - L² = 32
↓
L² - 12L + 32 = 0
↓
(L - 8)(L - 4) = 0
↓
L = 8 and 4
Step 4: Find the value of the second variable.
LW = 32
If L = 4, then..
4W = 32 → W = 8
L= 4
W = 8
This is false since the length should always be longer than the width.
If L = 8, then..
8W = 32 → W = 4
L = 8
W = 4
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