Question

something has gone wrong, i saw there are triangles but i only know 8.5 inches for one side and i wouldve used 11 inches for one side but the side lengths dont add up. how do you find the one side to utilize the pythagorean theorem? adobe_scan_jan_5_2026_1.pdf ·

a standard piece of paper is 8.5 inches wide by 11 inches long. suppose you fold the paper so one corner meets the opposite edge of the paper.
image of folding a rectangle to form a triangle
what is the length of the newly created edge (shown in red)?
length = ______________ inches (give your answer to two decimal places.)

re: question about #1 in homework 5.1
posted by: paul verschueren, mon, jan 5, 2026, 1:28 pm hide reply

thanks for asking! folding the paper that way would make two sides equal to 8.5 inches, so a = 8.5 and b = 8.5
the remaining 2.5 inches is not part of the triangle.
does that help?

Explanation:

Step1: Define triangle sides

When folding the paper, the right triangle formed has two legs: one is the width of the paper, $a=8.5$ inches, and the other is the remaining length of the long side after folding, $b=11-8.5=2.5$ inches. The red edge is the hypotenuse $c$.

Step2: Apply Pythagorean theorem

Use the formula $c=\sqrt{a^2 + b^2}$ to find the hypotenuse.

$$ c=\sqrt{8.5^2 + 2.5^2} $$

Step3: Calculate the values

First compute the squares: $8.5^2=72.25$, $2.5^2=6.25$. Sum them: $72.25+6.25=78.5$. Then take the square root: $\sqrt{78.5}\approx8.86$

Answer:

8.86 inches