Question

A holding pen for cattle must be square and have a diagonal length of 90 meters.

a. Find the length of a side of the pen.
b. Find the area of the pen.
a. The length of a side of the pen is

Answer 1

The length of a side of the square pen is approximately 63.64 meters, calculated using the Pythagorean theorem with a diagonal of 90 meters. The area of the pen is approximately 4052.97 square meters, calculated as the square of the side length.

Step-by-step explanation:

Finding the Length of a Side and the Area of a Square Pen

If a holding pen for cattle must be square and have a diagonal length of 90 meters, we can use the Pythagorean theorem to find the length of a side of the pen. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

To find the length of a side of the square (let's call it 's'), we can set up the equation:

• s2 + s2 = 902

Solving for 's' gives:

• 2s2 = 902
• s2 = (902)/2
• s = √((902)/2)
• s ≈ 63.64 meters

Therefore, the length of a side of the pen is approximately 63.64 meters.

Now, to find the area of the pen, we use the formula for the area of a square:

• Area = s2
• Area = (63.64)2
• Area ≈ 4052.97 square meters

The area of the pen is approximately 4052.97 square meters.