Question

kenneth takes a 7.1-inch by 3.8-inch sheet of paper and cuts from one corner of the paper to the diagonally opposite corner. now kenneth has two identical triangles. what is the perimeter of each triangle? if necessary, round to the nearest tenth.

Explanation:

Step1: Find the length of the diagonal

The paper is a rectangle with length \( l = 7.1 \) inches and width \( w = 3.8 \) inches. Using the Pythagorean theorem \( d=\sqrt{l^{2}+w^{2}} \), where \( d \) is the diagonal.
\[
d=\sqrt{7.1^{2}+3.8^{2}}=\sqrt{50.41 + 14.44}=\sqrt{64.85}\approx8.05
\]

Step2: Calculate the perimeter of the triangle

Each triangle has sides \( 7.1 \), \( 3.8 \), and \( d\approx8.05 \). The perimeter \( P \) is the sum of the sides.
\[
P = 7.1+3.8 + 8.05=18.95\approx19.0
\]

Answer:

\( 19.0 \)