In the box shown at the right, what is th length of the dashed line? There is a picture of a cube with a dashed line going through it diagonally. On top of the box a side is marked 12cm, on the side 8cm, and bottom 9cm.
To find the length of the dashed line in the cube, you can use the Pythagorean theorem.
1. Identify the three sides of the triangle formed by the dashed line:
a. One side is the 12cm side on top of the box.
b. Another side is the 8cm side on the side of the box.
c. The third side is the length of the dashed line.
2. Use the Pythagorean theorem to calculate the length of the dashed line:
a. The sum of the squares of the two shorter sides equals the square of the hypotenuse.
b. Let's label the shorter sides as a and b, and the hypotenuse (dashed line) as c.
c. So, we have a^2 + b^2 = c^2.
3. Substitute the given values into the Pythagorean theorem:
a. a = 12cm
b. b = 8cm
c. c = ?
Plugging in the values, we get:
(12cm)^2 + (8cm)^2 = c^2
Simplifying,
144cm^2 + 64cm^2 = c^2
208cm^2 = c^2
4. Take the square root of both sides to solve for c:
√(208cm^2) = √(c^2)
√208cm = c
Therefore, the length of the dashed line is approximately √208cm, which is about 14.42cm when rounded to two decimal places.
To find the length of the dashed line in the cube, we can use the Pythagorean theorem. The Pythagorean theorem states that, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the dashed line forms the hypotenuse of a right triangle inside the cube. We can use the given side lengths to find the length of the dashed line.
Let's label the side lengths of the cube:
The top side is 12cm, the side is 8cm, and the bottom side is 9cm.
Using the Pythagorean theorem, we can calculate the length of the dashed line. Let's label the dashed line as 'd'.
Applying the theorem:
d^2 = 12^2 + 8^2 + 9^2
Simplifying:
d^2 = 144 + 64 + 81
d^2 = 289
Taking the square root of both sides:
d = √289
d = 17cm
Therefore, the length of the dashed line is 17cm.