Question

6. A rectangular garden is 100 m long and 80 m wide. It is surrounded on its outside
by a uniformly broad path. If the area of the path is 1900 m, what is the width of
the path ?​

Answer 1

Answer:  5 m

Step-by-step explanation:

Length of garden = 100m and  Breadth of garden = 80m

Let the width of the path be w.

Outer length = (100 + w + w) = (100 + 2w) m

Outer breadth = (80 + w + w) = (80 + 2w) m

Area of path = area of outer rectangle - area of inner rectangle

                  = (100 + 2w) x (80 + 2w) - 100 x 80

                  = 160 w + 200 w + 4 w^2  = 4w^2 + 360 w

Hence,  4w^2 + 360 w = 1900

or, 4w^2 + 360 w - 1900 = 0

so we have,  w = 5, -95

Taking positive value only we have the width of the path is 5 m.