The width of the path when the length of the outer rectangle is 26+2x and width of it is 18+2x is 4 meters.
What is the area of a rectangle?
Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
A=a×b
Here, (a)is the length of the rectangle and (b) is the width of the rectangle
The length of the outer rectangle is 26+2x and width of it is 18+2x. The area of this rectangle is 884² m. Thus,
A=a×b
884=(26+2x)×(18+2x)
884=468+52x+36x+4x²
4x²+88x-416=0
Divide both side with 4,
x²+22x-104=0
x²+26x-4x-104=0
x(x+26)-4(x+26)=0
(x+26)(x-4)=0
x=-26,4
Take the positive value 4. The width of the path is equal to x which is 4 meters.
Hence, the width of the path when the length of the outer rectangle is 26+2x and width of it is 18+2x is 4 meters.
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