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Svetradugi [14.3K]
2 years ago
11

A graphic designer wants to create a rectangular graphic that has a 2-inch margin on each side and a 4-inch margin on the top an

d the bottom. The design, including the margins, should have an area of 392 square inches. What overall dimensions will
maximize the size of the design, excluding the margins?
(Hint: If one side of the design is x, then the other side is
392 divided by x.)
Mathematics
1 answer:
Anit [1.1K]2 years ago
8 0

The area of a shape is the amount of space the shape can occupy.

The dimension that maximizes the design is 20 inches by 20 inches

From the question, we have:

Area = 392in^2

Let the length and width of the graphic (without the margin) be l and w.

So, the dimension of the whole graphic is:

L = l + 2 + 2 = l +4

W = w + 4 + 4 = w +8

The area is then calculated as:

Area = L \times W

Area = (l + 4)  \times (w + 8)

Substitute Area = 392in^2

392 = (l + 4) \times (w + 8)

Make l + 4, the subject

l + 4 =\frac{392}{w + 8}

Subtract 4 from both sides

l  =\frac{392}{w + 8} - 4

The area of the design is:

A= lw

So, we have:

A  =(\frac{392}{w + 8} - 4)w

A  =\frac{392w}{w + 8} - 4w

Plot the graph of A  =\frac{392w}{w + 8} - 4w

From the graph (see attachment), the maximum is at:

(w,A) = (20,200)

Substitute (w,A) = (20,200) in A= lw

200 = l \times 20

Divide both sides by 20

l = 20

Hence, the dimension that maximizes the design (<em>excluding the margin</em>) is 20 inches by 20 inches

Read more about maximizing areas at:

brainly.com/question/3672366

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