Question

a rectangular garden 10m by 16m is to be surrounded by a concrete walk of uniform width. given that the area of the walk is 120 square metres, assuming the width of the walk to be x, from an equation in x and solve it to find the value of x.
please solve it with process pleaseeeer.

Answer 1

Given Length of the rectangular garden = 16m.

Given breadth of the rectangular garden = 10m.

We know that Area of rectangle = length * breadth

                                                      = 16 * 10

                                                      = 160m^2.


Given Area of the walk = 120m^2.

Total area = 160 + 120

                 = 280m^2.


The Length of the whole rectangle including concrete walk = 16 + 2x.

The breadth of the whole rectangle including concrete walk = 10 + 2x.


(16 + 2x) * (10 + 2x) = 280

160 + 32x+ 20x + 4x^2 = 280

4x^2 + 52x + 160 = 280

4x^2 + 52x + 160 - 280 = 0

4x^2 + 52x - 120 = 0

x^2 + 13x - 30 = 0

x^2 + 15x - 2x - 40 = 0

x(x + 15) - 2(x + 15) = 0

(x - 2)(x + 15) = 0

x = 2 (or) x = -15.


Since x cannot be -ve, so x = 2.

Therefore the value of x = 2.


Hope this helps!