Question

Kurt's garden is in the shape of a rectangle. The length is 10 ft less than twice the width, and the perimeter is 160 ft. Find the dimensions of the garden. *

Answer 1

Answer:

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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