Question

Norman bought 116 feet of fencing to put around his backyard. The backyard is a perfect square. Write an equation to find the dimensions of his backyard. Is the area big enough for a pool that is 900 feet x2 ​? Let s be the length of​ Norman's backyard.

Answer 1

The equation to find the dimensions of Norman's backyard is 4s = 116, where s represents the length and width of the backyard. The dimensions are 29 feet by 29 feet. The area of the backyard is 841 square feet, which is not big enough for a pool with an area of 900 feet.

Step-by-step explanation:

To find the dimensions of Norman's backyard, we can set up an equation based on the information given. Let s be the length of Norman's backyard, which is also the width since it's a perfect square. Since there are four sides in a square, the perimeter can be calculated as 4s. We are given that the perimeter is 116 feet, so we can write the equation as: 4s = 116. To find the dimensions, we need to solve for s by dividing both sides of the equation by 4: s = 116/4 = 29 feet. Therefore, the dimensions of Norman's backyard are 29 feet by 29 feet.

To determine if the backyard is big enough for a pool that is 900 square feet, we need to find the area of the backyard. The area of a square is calculated by multiplying the length by the width, so in this case, the area would be 29 ft x 29 ft = 841 square feet. Since 841 is less than 900, the area of Norman's backyard is not big enough to accommodate a pool with an area of 900 feet

Answer 2

116=perimeter
Since the backyard is a perfect square, the two sides are the same. Equation to find dimensions:
2x=116
x=58
To find the area of the backyard multiply x to itself.
58•58=3364
Area of total backyard: 3364 ft^2
Area of pool equation:
900•2=A
A= 1800
The area of the pool is less than the are of the backyard so yes, the pool will fit.