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.
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To find the length of d, we can use the Pythagorean Theorem.
We have the following information:
l = 30 in.
w = 20 in.
h = 18 in.
x = 36.1 in.
We can see that d is the hypotenuse of the right triangle formed by x, h, and d. So, we can use the Pythagorean Theorem to solve for d.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (d^2) is equal to the sum of the squares of the lengths of the other two sides (x^2 + h^2).
Substituting the given values, we have:
(x^2 + h^2) = d^2
(36.1^2 + 18^2) = d^2
(1303.21 + 324) = d^2
1627.21 = d^2
d ≈ √1627.21
d ≈ 40.3 inches
Therefore, the length of d is approximately 40.3 inches, rounded to the nearest tenth.