Question

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.

Answer 1

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.