Analyze the problem and answer the given questions.
The length of the rectangular garden is 2 m longer than its width and the area is 48 m².
1. What quadratic equation represents the area of the rectangular garden? Write the equation in terms of the width
of the garden.
2. Write the quadratic equation formulated in standard form. Solve the equation using any of the four methods of
solving quadratic equation.
3. What is the length of the garden? How about its width?
The length of the rectangular garden is 2 m longer than its width and the area is 48 m².
1. What quadratic equation represents the area of the rectangular garden? Write the equation in terms of the width
of the garden.
2. Write the quadratic equation formulated in standard form. Solve the equation using any of the four methods of
solving quadratic equation.
3. What is the length of the garden? How about its width?
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Answer:
1. x (x + 2) = 48 or x² + 2x = 48
2. x² + 2x - 48 = 0
3. Length = 8m
Width = 6m
Step-by-step explanation:
1. Width = x
Length = x + 2
Area = Length × Width
2. Standard Form: ax² + bx + c = 0
x² + 2x = 48
move constant to the left
x² + 2x - 48 = 0
3. Factor Method
x² + 2x - 48 = 0
x² + 8x - 6x - 48 = 0
x (x + 8) - 6 (x + 8) = 0
(x + 8) (x - 6) = 0
x₁ = |-8| = 8
x₂ = 6
Therefore, the length of the garden is 8m and the width is 6m.