Question

Miss sandy is fencing in her rectangular backyard which is 3x^2 feet wide and 4xy+5x^3y^2 feet long.

Find the perimeter of Miss Sandy’s yard.
How much fencing should Miss Sandy purchase?

Answer 1

Answer:So, Miss Sandy should purchase fencing with a length of 6x^2 + 8xy + 10x^3y^2 feet.

Explanation:

To find the perimeter of Miss Sandy's yard, we need to add up the lengths of all four sides of the rectangular yard.

The width of the yard is given as 3x^2 feet.

The length of the yard is given as 4xy + 5x^3y^2 feet.

To calculate the perimeter, we add up the four sides:

1. The top side has a length of 3x^2 feet.

2. The bottom side has a length of 3x^2 feet (same as the top side).

3. The left side has a length of 4xy + 5x^3y^2 feet.

4. The right side has a length of 4xy + 5x^3y^2 feet (same as the left side).

Adding up the lengths of all four sides, the perimeter of Miss Sandy's yard is:

(3x^2) + (3x^2) + (4xy + 5x^3y^2) + (4xy + 5x^3y^2)

Simplifying, we can combine like terms:

6x^2 + 8xy + 10x^3y^2

So, Miss Sandy should purchase fencing with a length of 6x^2 + 8xy + 10x^3y^2 feet.

Answer 2

10x³y²+6x²+8y square feet

Explanation:

The perimeter of a rectangle is the sum of all four sides.

Therefore,

Perimeter of rectangle= 2(width + length)

In this case:

The width of Miss Sandy's yard is 3x² feet and the length of her yard is 4xy+5x³y² feet.

Therefore, the perimeter of her rectangular yard is:

`\sf Perimeter = 2(3x^2 + 4xy+5x^3y^2 )`

Distribute 2 on the right side, we get:

`\sf Perimeter = 6x^2 + 8xy+10 x^3y^2`

Therefore, Perimeter of Miss Sandy’s yard is:

`\sf (10 x^3y^2+ 6x^2 + 8xy) ft^2`

So,

Miss Sandy should purchase 10x³y²+6x²+8y square feet of fencing.