Question

A straw is placed inside a rectangular box that is 3 inches by 3 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length of the straw, we can use the Pythagorean theorem.

Let the length of the straw be x.

Using the Pythagorean theorem, we have:

x^2 = 3^2 + 3^2 + 8^2
x^2 = 9 + 9 + 64
x^2 = 82

Taking the square root of both sides, we get:

x = √82

Therefore, the length of the straw is sqrt(82) inches.

Answer 2

ABCD is a kite, so start overline, A, C, end overline

AC
is perpendicular to⊥ start overline, D, B, end overline
DB
and D, E, equals, E, BDE=EB. Calculate the length of start overline, A, C, end overline
AC
, to the nearest tenth of a centimeter.

Answer 3

[AI-generated answer — Bot GPT 3.5]

If ABCD is a kite with AC perpendicular to DB and DE = EB, we can see that triangle ACD is a right triangle.

Let x be the length of AC.

Since DE = EB, triangle ADE is also a right triangle, where DAE = 90° and DE = EB.

This means that DB is the hypotenuse of triangle ADE, so according to the Pythagorean theorem, we can write:

AC^2 + DE^2 = AD^2
x^2 + (1/2)^2 = (2)^2
x^2 + 1/4 = 4
x^2 = 15/4
x = sqrt(15/4)
x = sqrt(15)/2
x ≈ 1.94 cm

Therefore, the length of AC to the nearest tenth of a centimeter is 1.9 cm.

Answer 4

A straw is placed inside a rectangular box that is 9 inches by 4 inches by 2 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the length of the straw, we can use the Pythagorean theorem.

Let the length of the straw be x.

The two sides of the rectangle that the straw passes through have lengths of 9 inches and 4 inches respectively, and the height of the box is 2 inches.

Using the Pythagorean theorem, we can set up the following equation:

x^2 = 9^2 + 4^2 + 2^2
x^2 = 81 + 16 + 4
x^2 = 101

Taking the square root of both sides, we get:

x = √101

Therefore, the length of the straw is approximately sqrt(101) inches.

Answer 6

A straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the length of the straw, we can use the Pythagorean theorem.

Let the length of the straw be x.

The two sides of the rectangle that the straw passes through have lengths of 5 inches and 5 inches respectively, and the height of the box is 8 inches.

Using the Pythagorean theorem, we can set up the following equation:

x^2 = 5^2 + 5^2 + 8^2
x^2 = 25 + 25 + 64
x^2 = 114

Taking the square root of both sides, we get:

x = √114

Therefore, the length of the straw is sqrt(114) inches.

Answer 8

A straw is placed inside a rectangular box that is 10 inches by 8 inches by 9 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the length of the straw, we can use the Pythagorean theorem.

Let the length of the straw be x.

The two sides of the rectangle that the straw passes through have lengths of 10 inches and 8 inches respectively, and the height of the box is 9 inches.

Using the Pythagorean theorem, we can set up the following equation:

x^2 = 10^2 + 8^2 + 9^2
x^2 = 100 + 64 + 81
x^2 = 245

Taking the square root of both sides, we get:

x = √245

Therefore, the length of the straw is sqrt(245) inches.

Answer 10

incorrect

Answer 11

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake in the previous calculation. Let's correct it:

Using the Pythagorean theorem for the rectangular box dimensions of 10 inches by 8 inches by 9 inches, the length of the straw (diagonal) can be found by:

x^2 = 10^2 + 8^2 + 9^2
x^2 = 100 + 64 + 81
x^2 = 245
x = √245

Therefore, the length of the straw is √245 inches.