Question

Julius designed a parallelogram-shaped banner with colorful tape around the edges and along the diagonal. The banner has a side with a length of 120 inches, a side with a length of 22 inches, and a diagonal of 122 inches. Which statement about the banner is true?

Answer 1

The statement that is true about the banner is that the length of the diagonal is 122 inches.

Step-by-step explanation:

To determine which statement about the banner is true, we can use the properties of a parallelogram. Since the banner has opposite sides that are equal in length, we can conclude that it is a parallelogram.

Using the given dimensions, we can calculate the length of the missing side by using the Pythagorean theorem. Let's name the missing side as c. Based on the given values, we have:

1. a = 120 inches
2. b = 22 inches
3. c = ?
4. a² + b² = c²
5. 120² + 22² = c²

Now we can solve for c:

• 14,400 + 484 = c²
• 14,884 = c²
• c = √14,884 ≈ 122 inches

Therefore, the statement that is true about the banner is that the length of the diagonal is 122 inches.