Question

A lawn in a city park is 50 feet long and 30 feet wide. A path with a width of x feet will be placed around the park. The city has enough

paving material to cover a path with an area of 900 square feet.

Answer 1

Julie should make the width of the sidewalk five feet

Explanation:

The complete question is as follows -

Julie wants to build a sidewalk of uniform width around her garden. Her garden is rectangular, and its dimensions are 20 feet by 30 feet. She has enough pavers to cover 900 square feet and wants to use all the pavers.

Complete the following statement. Round to the nearest tenth.

Julie should make the width of the sidewalk _____ feet.

Solution -

Let the width of the path be "X" feet.

Now Side of the park with path will be
`50 + 2X\\`

Width of the park would be
`30 + 2X`

Now Area of the path is
`900` square feet

So,

`(50+2X) (30 +2X) - (50 *30) = 900\\50 * 30 + 100 X + 60 X + 4X^2 - (50 *30) = 900\\160 X + 4X^2 = 900\\X^2 + 40 X = 225\\X^2 + 40 X -225 = 0\\X^2 + (45 X-5X) -225 = 0\\X ( X-5) + 45 (X-5) = 0\\X = 5`

Hence, the width of the park is 5 feet