Question

The length of a rectangular garden is 9 feet longer than its width. If the garden's perimeter is 206 feet, what is the area of the garden in square feet?

Answer 1

Area of rectangular garden is 2632 feet²

Explanation:

Given:-

• Length of Rectangular garden is 9 feet more than its width
• perimeterof garden is 206 feet.

To find :-

• The area of rectangular garden

Solution:-

Let the length of Rectangular garden be x + 9 feet and width be x feet .

We know that , the formula of Perimeter of rectangle is 2 ( L + B )

putting the known values to find the dimensions ,

2 ( L + B ) = 206 feet

2 ( x + 9 + x ) = 206 feet

4 x + 18 = 206 feet

x = 47 feet

putting the values of x in the equation ,

Length :- 56 feet

width :- 47 feet

Now , area of rectangular garden :- L×B

Area => 56×47 feet²

Area => 2632 feet²

Answer 2

• Area of rectangular garden is 2632 feet²

Explanation:

Given that length of Rectangular garden is 9 feet more than its width and perimeter of garden is 206 feet.

Let's assume length of Rectangular garden be x + 9 feet and width be x feet respectively. Firstly using the formula of Perimeter of rectangle we'll find the length and width of the garden.

`\\ \\ \dashrightarrow \: \: { \underline { \boxed{ \pink{ \sf {Perimeter _((rectangle)) = 2(L + W)}}}}} \\ \\`

Substituting the required values:

`\\`

`\dashrightarrow \sf \: \: 2(x + 9 + x) = 206 \\ \\`

`\dashrightarrow \sf \: \: 2x + 18 + 2x = 206 \\ \\`

`\dashrightarrow \sf \: \: 4x + 18 = 206 \\ \\`

`\dashrightarrow \sf \: \: 4x = 206 - 18 \\ \\`

`\dashrightarrow \sf \: \: 4x = 188 \\ \\`

`\dashrightarrow \sf \: \: x = (188)/(4 ) \\ \\`

`\dashrightarrow \sf \: \: x = 47 \\ \\`

Hence,

• Length of garden = x + 9 = 47 + 9 = 56 feet
• Width of garden = x = 47 feet

`\\`

Now,

`\\ \dashrightarrow \: \: { \underline { \boxed{ \pink{ \sf Area _((rectangle)) = Length * Width }}}} \\ \\`

Substituting the required values:

`\\`

`\dashrightarrow \sf \: \: Area = 56 * 47 \\ \\`

`\dashrightarrow \sf \: \: Area = 2632~ ft^2 \\ \\`

Hence,

• Area of rectangular garden is 2632 feet²