You build a box that is 4 feet long, 5 feet wide, and 8 feet high. The distance from the top left front corner to the top right back corner is ______.
I tried
a²= 4² + 5²
a²= 41
d² = 41 + 8²
d²= 105
d=+- 10.25
is this right?
d^2=4^2+5^2+8^2=16+25+64=105
d= sqrt 105
Now, your answer, notice I did not put -. How can a measurement on a box be negative?
To find the distance from the top left front corner to the top right back corner of the box, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two sides we want to find the distance between are the diagonal of the top face of the box (from the front left corner to the back right corner) and the height of the box.
First, let's find the length of the diagonal of the top face. You correctly used the Pythagorean theorem to calculate it:
a² = 4² + 5²
a² = 16 + 25
a² = 41
So the length of the diagonal of the top face is √41, which is approximately 6.4 feet.
Next, we want to find the distance from the top left front corner to the top right back corner. To do this, we need to consider the height of the box as the third side of a right triangle and use the Pythagorean theorem again:
d² = a² + height²
d² = 41 + 8²
d² = 41 + 64
d² = 105
Thus, you correctly calculated that d² = 105. However, when you took the square root, you made a small mistake. The square root of 105 is approximately 10.24, not ±10.25. Therefore, the distance from the top left front corner to the top right back corner of the box is approximately 10.24 feet.