Question

A vacant lot is being converted into a community garden. the garden and the walkway around its perimeter have an area of 378 ft2 . find the width of the walkway if the garden is 12 ft. wide by 15 ft. long

Answer 1

We have been given that the garden and the walkway around its perimeter have an area of 378 square feet.

Let us suppose the width of the walkway is x feet. Please see the attached image.

From the attached image, the area of the garden and the walkway around its perimeter is given by

Now, the area is given bt 378 square feet. Hence, we have

Explanation:

Answer 2

We have been given that the garden and the walkway around its perimeter have an area of 378 square feet.

Let us suppose the width of the walkway is x feet. Please see the attached image.

From the attached image, the area of the garden and the walkway around its perimeter is given by

`A=(15+2x)(12+2x)\\ \\ A=4x^2+54x+180`

Now, the area is given bt 378 square feet. Hence, we have

`4x^2+54x+180=378\\  \\ 4x^2+54x - 198=0\\ \\ \text{Using the quadratic formula, we have}\\ \\ x_(1,\:2)=(-54\pm √(54^2-4\cdot \:4\left(-198\right)))/(2\cdot \:4)\\ \\ x_(1,2)=3,-(33)/(2)\\ \\ \text{Width can't be negative}\\ \\ \text{Hence, we have} \\ x=3`

Therefore, the width of walkway is 3 feet.