A windowpane is 7 inches by 7 inches. What is the distance between opposite corners of the windowpane? If necessary, round to the nearest tenth.
To find the distance between opposite corners of the windowpane, we can use the Pythagorean theorem.
Let's call the length of one side of the windowpane a and the hypotenuse (distance between opposite corners) c.
Using the Pythagorean theorem, we have:
a^2 + a^2 = c^2
2a^2 = c^2
Substitute the length of one side of the windowpane (7 inches) for a:
2(7)^2 = c^2
2(49) = c^2
98 = c^2
Take the square root of both sides to find the distance between opposite corners:
c = √98
c ≈ 9.9 inches
Therefore, the distance between opposite corners of the windowpane is approximately 9.9 inches.