Question

A play school is designing two sand pits in ts play area . Each must have an area of 36 m2 . However , one of the sand pits must be rectangular , and the other must be square haped . What might be the dimensions of ach of the sand pits ?

Answer 1

Dimensions of square shaped pit = 6m
`*` 6m

Dimensions of rectangular pit = 1m
`*` 36m or 2m
`*` 18m or 3m
`*` 12m or 4m
`*` 9m

Explanation:

Given:

Two pits in the school playground area (one square shaped and one rectangular shaped).

Each pit must have an area = 36
`m^2`

To find:

Dimensions of each pit = ?

Solution:

First of all, let us have a look at the formula for area of a square and a rectangle:

`Area_(square) = (Side)^2`

`Area_(Rectangle) = Length* Width`

Now, let us try to find out dimensions of square:

`36 = Side^2\\\Rightarrow Side = 6\ m`

So, dimensions of Square will be 6m
`*` 6m.

Now, let us try to find out dimensions of rectangle.

`36 = Length* Width`

We are not given any restrictions on the Length and Width of the rectangle.

So, let us explore all the possibilities by factorizing 36:

`36 = 1 * 36\\36 = 2 * 18\\36 = 3 * 12\\36 = 4 * 9`

6
`*` 6 factors not considered because then it will become a square and which is not the required case.

Dimensions of rectangular pit = 1m
`*` 36m or 2m
`*` 18m or 3m
`*` 12m or 4m
`*` 9m