Question

A square garden is surrounded by a walkway of width X. If the area of the garden is 484 ft2 and the area covered by both the garden and the walkway (the entire square) is 784 ft2, what is the width of the walkway?

Answer 1

The width of the walkway is 3 feet, If the area of the garden is 484 $feet^{2}$ and the area covered by both the garden and the walkway (the entire square) is 784 $feet^{2}$.

Step-by-step explanation:

The given is,

                 Area of the garden is 484 $feet^{2}$

                 Area covered by both the garden and the walkway (the entire square) is 784 $feet^{2}$.

                Let, x - Width of the walkway

Step:1

                Formula to calculate area of square is,

                                $A= a^{2}$...........................(1)

                Where, r - Radius of square

Step:2

               For garden,

               A = 484 $feet^{2}$

               Equation (1) becomes,

                            $484=a^{2}$

               Take square root on both sides,

                               $a=\sqrt{484}$

                                a = 22 feet

               For garden and the walkway (the entire square),

               A = 784 $feet^{2}$

               Equation (1) becomes,

                            $784=a^{2}$

               Take square root on both sides,

                               $a=\sqrt{784}$

                                a = 28 feet

Step:3

                  Ref attachment,

                  Side of garden and the walkway =

                             Side of garden + 2 (width of the walkaway)....(1)

                                                 28 = 22 + 2 ( x )

                                             2 ( x ) =   28 - 22

                                                       = 6

                                                    $x = \frac{6}{2}$

                                        Width, x = 3 feet

Result:

          The width of the walkway is 3 feet, If the area of the garden is 484 $feet^{2}$ and the area covered by both the garden and the walkway (the entire square) is 784 $feet^{2}$.