Question

Tasha assembled a picture frame that is advertised as rectangular. The completed frame is 14 inches long and 10 inches wide. She measured the diagonal length across the frame as 20 inches. Which best explains why the frame cannot actually be rectangular?

Answer 1

The frame cannot be rectangular because the measured diagonal length across the frame does not match the expected length based on the given dimensions.

Step-by-step explanation:

The completed frame cannot actually be rectangular because the measured diagonal length across the frame does not match the expected length based on the given dimensions of the length and width. In a rectangular frame, the length, width, and diagonal form a right triangle.

Using the Pythagorean Theorem, we can determine the expected diagonal length of a rectangular frame with length = 14 inches and width = 10 inches:

`diagonal^2 = length^2 + width^2`

`diagonal^2 = 14^2 + 10^2`

= 196 + 100

= 296

= √296

diagonal ≈ 17.17 inches

Since the measured diagonal length is 20 inches, which is larger than the expected diagonal length, the frame cannot be a rectangle.

Answer 2

the diagonal of a rectangle is square root of (w^2 +l^2)

so square root of (14^2 +10^2) = 17.2 inches

since 20" is longer than 17.2 it can't be a rectangle