Question

Josh has a garden in the shape of a square with a perimeter of 96 feet. He plans to plant tomatoes along the diagonal. How long is the diagonal of the garden?

a. 48 feet
b. 60 feet
c. 72 feet
d. 84 feet

Answer 1

To find the length of the diagonal of the square garden, we can use the Pythagorean theorem. First, we find the length of one side of the square garden by solving the equation 4s = 96. Then, we use the Pythagorean theorem d^2 = 24^2 + 24^2 = 2(24^2) to find the length of the diagonal, which is approximately 33.94 feet.

Step-by-step explanation:

To find the length of the diagonal of the square garden, we need to use the formula for the diagonal of a square.

The perimeter of a square is equal to 4 times the length of one side, so let's represent the length of one side as 's'.

We are given that the perimeter of the garden is 96 feet, so the equation is 4s = 96.

Solving for 's', we divide both sides of the equation by 4 to find that s = 24 feet.

Now, to find the length of the diagonal, we can use the Pythagorean theorem, which states that the square of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the two legs (in this case, the sides of the square).

The length of one side is 24 feet, so using the Pythagorean theorem, we have d^2 = 24^2 + 24^2 = 2(24^2).

Taking the square root of both sides, we find d = sqrt(2(24^2)) = 24(sqrt(2)) = 24(1.41) ≈ 33.94 feet.

So, the length of the diagonal of the garden is approximately 33.94 feet.