The Pythagorean Theorem in Three Dimensions Practice
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Question
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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.
To find the length of d in the given rectangular prism, we can use the Pythagorean Theorem in three dimensions. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is d, and the other two sides are x and h. Using the Pythagorean Theorem, we can write:
d^2 = x^2 + h^2
Now, let's substitute the given values into the equation:
d^2 = (36.1 in)^2 + (18 in)^2
Calculating this equation, we get:
d^2 = 1303.21 in^2 + 324 in^2
d^2 = 1627.21 in^2
To find the length of d, we need to take the square root of both sides:
d = sqrt(1627.21)
Calculating this, we find that d is approximately 40.34 inches.
Therefore, the length of d is approximately 40.34 inches.
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.
no use The Pythagorean Theorem
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.
nope
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.