1. ## Word problem

Q) A rectangular field , 70m long and 50m wide, has a path of uniform width around it .If the area of the path is 1024m^2 , find the width of the path.

Solution let x be the uniform width of the path

According to the given condition,

(50+2x)(70+2x)-1024=50*70

...............................

and the answer comes out to be 4m after solving this.

I have problem in that how the bold equation is formed ?

2. You know the area of a rectangle to be $\displaystyle A = lw$ and so $\displaystyle A_{f} = 50 \times 70 \text{ m}^2$

Like they did, let x be the width of the path.

Now consider the length of the field and path - it is going to be the length of the field (70) plus the width of the path at both ends (2x) which is equal to $\displaystyle l = 70+2x$
Do the same for the width and the path: $\displaystyle w = 50+2x$

The area of the field+path is also length x width: $\displaystyle A_{f+p} = (50+2x)(70+2x)$

The area of the path will be the area of the field+path minus the area of the filed: $\displaystyle A_p = A_{p+f} - A_f$ - you are given that $\displaystyle A_p = 1024$ and so the equation is $\displaystyle 1024 = (50+2x)(70+2x) - 50 \times 70$

Which can be rearranged into $\displaystyle (50+2x)(70+2x) - 1024 = 50 \times 70$

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# a rectangular field is 70m long and 50m wide has a path of uniform width arround it if the area of the path is 1024 m^2 find the width of path

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