Question

Arif’s backyard is 24 by 30 meters. He wants to put a flower garden in the middle of the backyard, leaving a strip of grass of uniform width around the flower garden. Arif must have 368 meters squared of grass. Under these conditions what will the length and width of the garden be?

Answer 1

The length and width of garden are 16 meters and 22 meters

Solution:

Step 1:

Find the area of backyard

Given that, backyard is 24 by 30 meters

Area = length x width

Area = 24 x 30 = 720

Thus area of backyard is 720 square meters

Step 2:

Given that area of grass = 368 square meter

Then, area of garden = area of backyard - area of grass

area of garden = 720 - 368

area of garden = 352 square meter

Step 3:

Find the dimensions of garden

Let "x" be the width of strip of grass

Then, the dimensions of garden are:

Length of garden = 24 - 2x

Width of garden = 30 - 2x

Then,

area of garden = (24 - 2x)(30 - 2x)

`(24 - 2x)(30 - 2x) = 352\\\\720 - 48x -60x + 4x^2 - 352 = 0\\\\4x^2 -108x + 368 = 0\\\\x^2-27x + 92=0`

Factor the left side

(x - 23)(x - 4) = 0

By zero factor property,

x = 23 or x = 4

The solution x = 23 makes the dimensions of garden negative, so we reject it

So the dimensions of garden are:

Length = 24 - 2x = 24 - 2(4) = 24 - 8 = 16

Width = 30 - 2x = 30 - 2(4) = 30 - 8 = 22

Thus length and width of garden are 16 meters and 22 meters