If the planted border has an area of 504 square feet, find x, the width of the border. (include mathematical work))

Question

Jennie built an outdoor area that was 25 ft by 40 ft. The area included a patio and border around it. The border has the same width of x all the way around the patio.

Answer 1

Always draw a picture. An outer square with dimensions of

40 x 25

an inner square dimensions unknown. We are looking for x, the width of the border

a simple 40x25 finds the total area, BUT for the area of the border, we must subtract the overlapping ends, giving us

25 - 2x, the length of the sides.

this gives us the equation:

504 = 2*40*x + 2(25 - 2X)* x

simplifying we get the quadratic equation:

0 = 4x² - 50x - 80x + 504 further simplifying and dividing by 2:

0= 2x² - 65x + 252

using the quadratic formula, you get 2 answers. Only one will make sense and give you 540 when put back into the equation.

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Answer 2

Restatement of the facts of the problem: The entire area is 25 feet by 40 feet. There is a border with a uniform-width walkway around the outside of the area. The area of the border is 504 square feet.

The width of the border is the same on each of the four sides: 25x on two opposite sides, and 40x on the other two sides. Each of four corners has an area of x² square feet.

A rough diagram:

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25x+25x+40x+40x+4x² = 504

50x + 80x + 4x² = 504

130x + 4x² = 504

Subtract 504 from both sides and arrange in standard form for a quadratic:

4x² + 130x -504 = 0

Using the quadratic formula:

x = -36 and x = 3.5; discard the negative value because we are looking for distances.

The border is 3.5 feet wide. Check this value to see it solves the above equations.

Answer 3

If I understand this correctly... the area with the plants (not including the walkway) has an area of 504 square feet, and the area including the walkway is 25 x 40... right?