The maximum size envelope that can be mailed at the large envelope rate 3 in.longer than it is wide. The area is 180 in^2. Find

Question

sweet [91]

3 years ago

12

The maximum size envelope that can be mailed at the large envelope rate 3 in.longer than it is wide. The area is 180 in^2. Find

the length and width.

Mathematics

1 answer:

choli [55] · Answer 1 · 2022-07-24T09:24:12+03:00

Length = 15 inches

Width = 12 inches

Further explanation:

We have to construct equation to solve the situation.

Let x be the width of the rectangle

Then, x+3 will be the length 3 in.longer than it is width

The formula for area is:

$Length*Width = Area\\x(x+3) = 180\\x^2+3x = 180\\x^2 +3x - 180 = 0\\x^2 +15x - 12x -180 = 0\\x(x+15)-12(x+15)=0\\(x-12)(x+15) = 0\\x = 12\ and\ x=-15$

As the length measurements cannot be negative, we will only use the positive value

so, width = 12 inches

and Length = x+3 = 12+3 = 15 inches

Keywords: Rectangle area, finding areas of rectangles

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