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.
To find the length of d, we can use the Pythagorean theorem.
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 triangle formed by d, x, and the height h is a right triangle.
We can set up the equation as follows:
d^2 = x^2 + h^2
Substituting the given values:
d^2 = (36.1)^2 + (18)^2
d^2 = 1303.21 + 324
d^2 = 1627.21
Taking the square root of both sides to solve for d:
d = sqrt(1627.21)
d ≈ 40.3
Therefore, the length of d is approximately 40.3 inches.
To find the length of "d" in the given three-dimensional rectangular prism, we'll use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have right-angled triangles formed by the edges of the prism. The hypotenuse of one of these triangles is "d," and the other two sides are "x" and "w." According to the Pythagorean theorem, we have:
d^2 = x^2 + w^2
Plugging in the given values, we have:
d^2 = (36.1)^2 + (20)^2
Calculating this expression:
d^2 = 1303.21 + 400
d^2 = 1703.21
To find the length of "d," we take the square root of both sides:
d = √(1703.21)
d ≈ 41.3 inches
Therefore, the length of "d" in the given three-dimensional rectangular prism is approximately 41.3 inches.
To find the length of d, we can use the Pythagorean theorem. According to the given information, we have a right triangle with the lengths of the two sides adjacent to the right angle, l and x, and the hypotenuse d.
Using the Pythagorean theorem:
l^2 + x^2 = d^2
Substituting the given values:
(30 in.)^2 + (36.1 in.)^2 = d^2
900 in^2 + 1303.21 in^2 = d^2
2203.21 in^2 = d^2
Taking the square root of both sides:
d = √2203.21 in^2
Calculating the square root:
d ≈ 46.9 in
Therefore, the length of d is approximately 46.9 inches.