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A farmer has a squared field of area $x^{2} - 26 x + 169$ square units. He divided the field into two equal parts. Then find the sides of the field in terms of x.

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x - 10

and

\frac{x + 13}{4}

x - 5

and

\frac{x - 4}{2}

x + 13

and

\frac{x + 13}{4}

x - 13

and

\frac{x - 13}{2}

answer is D.

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Detailed Solution

Given a squared field of area is,

x^{2} - 26 x + 169

Suppose side of square field= a
As, the area of squared field is,

\Rightarrow A = {(side)}^{2}

\Rightarrow A = x^{2} - 26 x + 169

\Rightarrow a^{2} = x^{2} - 26 x + 169

\Rightarrow a^{2} = x^{2} - 2 (13) (x) + (13)^{2}

\Rightarrow a^{2} = (x - 13)^{2}

[

Since (m - m)^{2} = m^{2} - 2 mn + n^{2}]

\Rightarrow a = x - 13

Here, we have the square field CDEF.
Draw a line AC which divides the CDEF in two equal parts.
Here, AC=AF=BD=BE
So, width of new rectangle,

\Rightarrow s = \frac{x - 13}{2}

Thus, the length of sides of field are

x - 13

and

\frac{x - 13}{2}

.
Hence, the correct option is 4.

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