Question
The Pythagorean Theorem in Three Dimensions Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
2 of 52 of 5 Items
Question
Use the image to answer the question.
An illustration shows a three dimensional rectangular prism with labeled parts. The top, front and right sides are visible. The bottom, left, and rear sides are not visible, but their positions are indicated by dashed lines. The vertical edge joining the front and left sides is labeled h. A right angle is indicated where that edge meets the front base edge. The front base edge is labeled l. A right angle is indicated where that edge meets the right base edge. The right base edge is labeled w. Two dotted lines extend from the vertex at the back right side of the prism through the interior. The first dotted line extends up to the vertex at the front left side and is labeled d. The second dotted line extends diagonally across the base to the vertex at the front left side where the perpendicular height line meets the base edge and is labeled x.
Given l=30 in. , w=20 in. , h=18 in. , and x=36.1 in. , find the length of d . Round the answer to the nearest tenth.
(1 point)
in.
Answers
Answer
no use The Pythagorean Theorem
Answer
nope
Answered by
GPT 3.5
To find the length of d, we can use the Pythagorean Theorem in three dimensions.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the line connecting the back right vertex to the front left vertex, which is line d. The other two sides are the line connecting the front left vertex to the front base edge (l), and the line connecting the front base edge to the right base edge (w).
Using the Pythagorean Theorem, we have the equation:
d^2 = l^2 + w^2
Substituting the given values:
d^2 = 30^2 + 20^2
d^2 = 900 + 400
d^2 = 1300
Taking the square root of both sides to solve for d:
d = √1300
d ≈ 36.06
Rounding to the nearest tenth, the length of d is approximately 36.1 inches.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the line connecting the back right vertex to the front left vertex, which is line d. The other two sides are the line connecting the front left vertex to the front base edge (l), and the line connecting the front base edge to the right base edge (w).
Using the Pythagorean Theorem, we have the equation:
d^2 = l^2 + w^2
Substituting the given values:
d^2 = 30^2 + 20^2
d^2 = 900 + 400
d^2 = 1300
Taking the square root of both sides to solve for d:
d = √1300
d ≈ 36.06
Rounding to the nearest tenth, the length of d is approximately 36.1 inches.
Answered by
GPT 3.5
I apologize for the confusion. To find the length of d using the Pythagorean Theorem, we need to consider the right triangle formed by the vertical edge (height) h, the base edge l, and the diagonal line d.
According to the Pythagorean Theorem:
d^2 = h^2 + l^2
Substituting the given values:
d^2 = 18^2 + 30^2
d^2 = 324 + 900
d^2 = 1224
Taking the square root of both sides to solve for d:
d ≈ √1224
d ≈ 34.99
Rounding to the nearest tenth, the length of d is approximately 35.0 inches.
According to the Pythagorean Theorem:
d^2 = h^2 + l^2
Substituting the given values:
d^2 = 18^2 + 30^2
d^2 = 324 + 900
d^2 = 1224
Taking the square root of both sides to solve for d:
d ≈ √1224
d ≈ 34.99
Rounding to the nearest tenth, the length of d is approximately 35.0 inches.
Answered by
GPT 3.5
I apologize for the previous incorrect response. Let's try again.
To use the Pythagorean Theorem to find the length of d, we need to consider the right triangle formed by the vertical edge (height) h, the base edge l, and the diagonal line d.
According to the Pythagorean Theorem:
d^2 = h^2 + l^2
Substituting the given values:
d^2 = 18^2 + 30^2
d^2 = 324 + 900
d^2 = 1224
Taking the square root of both sides to solve for d:
d ≈ √1224
d ≈ 34.99
Rounding to the nearest tenth, the length of d is approximately 35.0 inches.
To use the Pythagorean Theorem to find the length of d, we need to consider the right triangle formed by the vertical edge (height) h, the base edge l, and the diagonal line d.
According to the Pythagorean Theorem:
d^2 = h^2 + l^2
Substituting the given values:
d^2 = 18^2 + 30^2
d^2 = 324 + 900
d^2 = 1224
Taking the square root of both sides to solve for d:
d ≈ √1224
d ≈ 34.99
Rounding to the nearest tenth, the length of d is approximately 35.0 inches.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.