The length and breadth of a rectangular park are in the ratio of 8:5. A path 1.5 m wide running all around the outside of an area of 594 m2. The dimensions of the park are ____ m and ____m.

Question

Accepted Answer

Concept- The dimensions of the park are 120,75.
Given are the ratio of dimensions of a rectangular park and the area of a path 1.5 m wide running all around the park.We will assume the dimensions of the park to by multiplying the individual proportions to a common constant, say

and we will calculate the area of the park based on the variable only.
As the width of the path is given, we will add 2 times the width of the path to both the length and breadth of the park and calculate the total area of (park + path). Then, we will subtract the total area of (park + path) from the area of rectangular park, which will give us the area of the path and we will equate it to 594 m2 (as already information provided in the question statement).This will give us an equation, solving which, we will obtain our desired answer.
Area of a rectangle = (l × b) where, “l” is the length of the rectangle and “b” is the breadth of the rectangle.
Given, the ratio of dimensions of a rectangular park is 8:5. Let us assume the length of the park to be (l = 8

) and breadth to be (b = 5

).
Then, area of the park (Apark) [rectangle ABCD]

Also given, a path 1.5 m wide is running all around the outside of the park of 594 m2. The total area of (park + path) also makes a rectangle,