Question

The figures below show sketches of Earl's and Dylan's flower gardens. If the perimeter of each of their gardens is the same, what is the length and width of Earl's garden?​

Answer 1

Answer:

$length = 12 ft$

$width = 8 ft$

Step-by-step explanation:

Earl's garden:

$length = (x + 6) ft$

$width = (x + 2) ft$

$perimeter = 2(length) + 2(width)$

$perimeter = 2(x + 6) + 2(x + 2)$

$perimeter = 2x + 12 + 2x + 4 = (4x + 16) ft$

Dylan's garden:

$length = (2x - 2) ft$

$width = (x + 4) ft$

$perimeter = 2(length) + 2(width)$

$perimeter = 2(2x - 2) + 2(x + 4)$

$perimeter = 4x - 4 + 2x + 8 = (6x + 4) ft$

Generate an equation to solve for the value of x.

Since the perimeters of both gardens are the same, therefore:

$6x + 4 = 4x + 16$

Collect like terms

$6x - 4x = - 4 + 16$

$2x = 12$

Divide both sides by 2

$x = 6$

Earl's garden:

$length = (x + 6) ft$

Plug in the value of x

$length = 6 + 6 = 12 ft$

$width = (x + 2) ft = 6 + 2 = 8 ft$