A rectangular sandbox is surronded on all sides by a strip of grass that is 5 fe

facas9

facas9

Answered question

2021-09-13

A rectangular sandbox is surronded on all sides by a strip of grass that is 5 feet wide on all sides. The length of the sandbox is 4 feet more than the width, and the total area for the sandbox and the grass is 189 square feet. Find the dimensions of the sandbox.
The length of the sandbox is ___ feet and the width is ___ feet.
(Simplify your answers. Type integers or decimals rounded to the nearest hundredth as needed.)

Answer & Explanation

Viktor Wiley

Viktor Wiley

Skilled2021-09-14Added 84 answers

Step 1
Let the width of the sandbox is x feet.
Therefore length of the sandbox is x+4.
Total length of the sandbox is (x+4)+5+5=x+14.
Total width be x+5+5=x+10
Step 2
Total area for the sandbox and the grass is 189 square feet
(x+14)(x+10)=189
x2+24x+140189=0
x2+24x49=0
Determine the value of x from the quadratic equation above.
x=24±(24)24(1)(49)2(1)
x=24±27.782
x=1.89,25.89
Therefore the width of the sandbox is 1.89 feet and length of the sandbox is 1.89+4=5.89 feet.

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