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UkoKoshka [18]
3 years ago
7

A rectangular garden originally measured 5 feet by 10 feet as shown below.a path was created by increasing each side of the orig

inal rectangle by x-feet on both sides.if the area of the path that rings the garden is 54 square feet,find the value of x.
Mathematics
1 answer:
kotegsom [21]3 years ago
3 0
The area is given by
 A = (5 + 2x) * (10 + 2x) - 50
 Rewriting we have:
 A = 50 + 10x + 20x + 4x ^ 2 -50
 Rewriting we have:
 A = 4x ^ 2 + 30x
 Substituting the value of the area we have:
 54 = 4x ^ 2 + 30x
 Rewriting:
 4x ^ 2 + 30x - 54 = 0
 We look for the roots:
 x1 = -9
 x2 = 3/2
 We take the positive root:
 x2 = 3/2
 Answer:
 
the value of x is:
 
x = 3/2
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