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A garden 7 m by 12 m will be expanded by planting a border of flowers.
The border will be of the same width around the entire garden and has an area of 92 square meters.
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The question absents in this post, which is inaccuracy
and disrespect to tutors, both in the same time.
The garden is a rectangle 7 m by 12 m. Its area is 7*12 = 84 m^2.
Let w be the uniform width of the border of flowers around the garden.
The extended garden is a rectangle of dimensions (7+2x) by (12+2x) meters.
The area of the extended garden is (7+2x)*(12+2x) m^2.
The difference of these two areas is the area of the border around the garden.
So, we write this equation
(7+2x)*(12+2x) - 84 = 92 square meters. (1)
At this point, the setup is complete.
Now our goal is to find x from this equation.
Simplify it
84 + 24x + 14x + 4x^2 - 84 = 92.
4x^2 + 38x - 92 = 0,
2x^2 + 19x - 46 = 0.
Use the quadratic formula
= = = .
One root is positive, the other root is negative.
Naturally, we discard the negative root and accept the positive root
x = = = 2 meters.
ANSWER. The uniform width of the border around the garden is 2 meters.
CHECK. We check if equation (1) is correct.
Its left side is (7+2*2)*(12+2*2) - 84 = use your calculator = 92 m^2,
precisely as the given area of the border.
Solved.
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To see many other similar solved problems, look into the lessons
- Problems on the area and the dimensions of a rectangle surrounded by a strip
- Cynthia Besch wants to buy a rug for a room
- Problems on a circular pool and a walkway around it
in this site.
Learn the subject from there.