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16 ft
8. GARDEN A rectangular garden is 12 feet across and 16 feet long. It is
surrounded by a border of mulch that is a uniform width, x. The
maximum area for the garden, plus border, is 285 ft.
a. Write a polynomial equation to represent the situation.
12 it
b. Write and solve a system of equations.
c. What are the dimensions of the garden plus border?

Sagot :

Raphealnwobiidn

The dimensions of the border is 1.5 feet for the garden

A rectangle is a quadrilateral with four sides and four angles in which opposite sides are equal and parallel.

The area of a rectangle = Length * breadth

Given that length of garden = 16 ft., width of garden = 12 ft.

It is surrounded by a mulch of width x, hence:

New length = 16 + x + x = 16 + 2x

New width = 12 + x + x = 12 + 2x

The area of garden = 16 + 2x(12 + 2x) = 192 + 56x + 4x²

Since the maximum area is 285 ft, hence:

192 + 56x + 4x² = 285

4x² + 56x - 93 = 0

x = 1.5 feet

The dimensions of the border is 1.5 feet

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