Question

the playground at school is rectangular, and each dimension is a whole number. the playgrounds area is 3772 square feet, and it’s perimeter is 256 feet. what are the dimensions of the playground?

Answer 1

Length=82

width= 46

Explanation:

Given:

Area of Rectangle}= 3772

Perimeter of Rectangle=256

`\textrm{Formula of Perimeter of rectangle} = 2(length+width)`

Substituting the values we get:

`2(l+b)=256\\l+b=(256)/(2)\\l+b=128\\l=128-b`

Now

`\textrm{Formula of Area of rectangle}= length* width`

Substituting the values we get:

`l * b= 3772`

Now from above equation derived for length we will substitute value of l in the above equation we will get.

`b(128-b)=3772\\128b-b^(2) =3772\\`

Now taking left hand side to right handside we get

`b^(2) -128b+3772=0\\b^(2)-46b-82b+3772=0\\b(b-46)-82(b-46)=0\\(b-46)(b-82)=0\\`

Now solving for both equation we get.

`b-46=0 \\ b=46`

`b-82=0\\b=82`

from above we can conclude that

length=82

width=46