Question

The dimension of a rectangular garden are 12 1/2 feet by 16 3/4 feet. If 1 5/8 feet is added to all the sides, find the new dimensions of the garden.

Answer 1

Answer: The new dimensions of the garden are
`13(1)/(8)\ feet\ and\ 17(3)/(8)\ feet`

Explanation:

Since we have given that

Old length of rectangular garden =
`12(1)/(2)=(25)/(2)\ feet`

Old breadth of rectangular garden =
`16(3)/(4)=(67)/(4)\ feet`

If
`(5)/(8)` feet is added to all the sides.

So, New length of rectangular garden is given by

`(25)/(2)+(5)/(8)\\\\=(100+5)/(8)\\\\=(105)/(8)\\\\=13(1)/(8)\ feet`

New breadth of rectangular garden is given by

`(67)/(4)+(5)/(8)\\\\=(134+5)/(8)\\\\=(139)/(8)\\\\=17(3)/(8)\ feet`

Hence, the new dimensions of the garden are
`13(1)/(8)\ feet\ and\ 17(3)/(8)\ feet`

Answer 2

`L=15\tfrac{6}{8} \ feet`

`B=20 \ feet`

Explanation:

Given that the dimensions of a rectangular field is (in feet)

`l=12\tfrac{1}{2}=(12 * 2 +1)/(2)=(25)/(2)`

`b=16\tfrac{3}{4}=(16 * 4 +3)/(4)=(67)/(4)`

Now we are being told that
`1\tfrac{5}{8}` feet is added to each side. Hence New Dimensions will be

`1\tfrac{5}{8}=(1 * 8 +5)/(8)=(13)/(8)`

`L = (25)/(2)+(13)/(8)+(13)/(8)`

`L=(25 * 4)/(2 * 4)+(13)/(8)+(13)/(8)`

`L=(100)/(8)+(13)/(8)+(13)/(8)`

`L= (100+13+13)/(8)`

`L= (126)/(8)`

`L=15\tfrac{6}{8}`

`B= (67)/(4)+(13)/(8)+(13)/(8)`

`B= (67* 2)/(4* 2)+(13)/(8)+(13)/(8)`

`B= (134)/(8)+(13)/(8)+(13)/(8)`

`B= (134+13+13)/(8)`

`B=(160)/(8)`

`B=20`

Hence New Dimensions are

`L=15\tfrac{6}{8} \ feet`

`B=20 \ feet`