se 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.
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To find the length of d, we can use the Pythagorean Theorem. We know that d is the hypotenuse of a right triangle formed by the edges l, w, and h.
Using the Pythagorean Theorem, we have:
d^2 = l^2 + w^2 + h^2
Substituting the given values, we have:
d^2 = 30^2 + 20^2 + 18^2
d^2 = 900 + 400 + 324
d^2 = 1624
Taking the square root of both sides, we have:
d ≈ √1624
d ≈ 40.3 in.
Therefore, the length of d is approximately 40.3 inches.
To find the length of d, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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, d is the hypotenuse and we know the lengths of the other two sides, x and h.
Using the Pythagorean theorem, we can write the equation:
d^2 = x^2 + h^2
Plugging in the given values, we have:
d^2 = (36.1 in)^2 + (18 in)^2
Calculating this, we get:
d^2 = 1303.21 in^2 + 324 in^2
d^2 = 1627.21 in^2
To find the length of d, we take the square root of both sides of the equation:
d = √1627.21 in^2
Simplifying this, we find:
d ≈ 40.3 in
Therefore, the length of d is approximately 40.3 inches.
To find the length of d, we can use the Pythagorean theorem. In the prism, we have a right triangle formed by the three edges: d, h, and x.
Using the Pythagorean theorem, we can write the equation:
d^2 = h^2 + x^2
Substituting the given values, we have:
d^2 = (18 in.)^2 + (36.1 in.)^2
Calculating this equation will give us the value of d^2.
d^2 = 324 + 1303.21
d^2 = 1627.21
Now, to find the length of d, we take the square root of both sides of the equation:
d = √1627.21
Calculating this equation will give us the value of d.
d ≈ 40.34 in.
Therefore, the length of d is approximately 40.34 inches (rounded to the nearest tenth).