Answer
Width of walkway,$x=3.1$ ft
Work Step by Step
Area of the walkway=$(2x+42)(2x+26)-26 \times 42$
Thus, $4x^2+136x=460$
Re-write the equations as: $x^2+34x=115$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=34$
To complete the square, add $\dfrac{(34)^2}{4}=289$ on both sides.
$x^2+34x+289=115+289$
$\implies (x+17)^2=404$
Neglecting the negative sign, we have
$\implies (x+17)=20.1$
$x=3.1$ ft
Width of walkway,$x=3.1$ ft
