A rectangular flower garden has a length that is 5 feet less than twice its width. A 5-foot brick border is added around the garden, and the area of the garden and the brick border is a total of 225 square feet. Find the dimensions of the garden without the brick border
Answers
If the area of the garden and the brick border is a total of 225 square feet, then the dimensions of the garden without the brick border will be 5 ft x 5 ft.
Step-by-step explanation:
Let the width or breadth of the rectangular garden be denoted as “x” ft
Then the length of the garden will be l = (2x – 5) ft
It is given that a brick border of 5 ft width is added around the garden .
So,
The new length of the garden including the border will be = l + 2w = (2x – 5) + (2*5) = (2x + 5) ft
The new breadth of the garden including the border will be = x + 2w = x + 2*5 = (x + 10) ft
It is given that,
The area of the garden and the brick border in a total = 225 square feet
⇒ [new length] * [new breadth] = 225
⇒ (2x + 5) * (x + 10) = 225
⇒ 2x² + 20x + 5x + 50 = 225
⇒ 2x² + 25x -175 = 0
⇒ 2x²– 10x + 35x – 175 = 0
⇒ 2x(x-5) + 35(x-5) = 0
⇒ (x-5)(2x-35) = 0
⇒ x = 5 or -35/2
neglecting the negative value
⇒ x = 5 ft ← breadth of the flower garden
∴ length of the flower garden = 2x – 5 = (2*5) – 5 = 10-5 = 5 ft
Thus, the dimensions of the garden without the brick border are 5 ft x 5 ft.
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