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)
To find the length of d, let's use the Pythagorean theorem.
We know that x, h, and d form a right triangle.
We have the values of x and h: x = 36.1 in. and h = 18 in.
Using the Pythagorean theorem, we can find the length of d:
d² = x² + h²
d² = (36.1 in.)² + (18 in.)²
d² = 1303.21 in² + 324 in²
d² = 1627.21 in²
Taking the square root of both sides, we get:
d ≈ √1627.21
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 triangle, the square of the length of the hypotenuse (in this case, d) is equal to the sum of the squares of the lengths of the other two sides (in this case, x and h).
Using the given values, we have:
x = 36.1 in.
h = 18 in.
We can substitute these values into the Pythagorean theorem equation:
d^2 = x^2 + h^2
d^2 = (36.1 in.)^2 + (18 in.)^2
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 = sqrt(1627.21 in^2)
d ≈ 40.34 in.
Therefore, the length of d is approximately 40.34 inches.
To find the length of d, we can use the concept of the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In the given illustration of the rectangular prism, we can see that the length l, width w, and height h form a right triangle. The side l represents the base, the side w represents the vertical edge joining the front and left sides, and the side h represents the perpendicular height from the right base edge to the vertex at the front left side.
To get the length of d, we need to find the diagonal line that connects the vertex at the back right side to the front left side. This diagonal line can be represented by the hypotenuse of a right triangle, where the two other sides are the height h and the distance x along the base.
Using the Pythagorean theorem, we can set up the equation:
d^2 = h^2 + x^2
Now, let's substitute the given values into the equation:
d^2 = (18 in.)^2 + (36.1 in.)^2
Simplifying this equation gives:
d^2 = 324 in^2 + 1303.21 in^2
d^2 = 1627.21 in^2
To find the length of d, we can calculate the square root of both sides:
d = √(1627.21 in^2)
d ≈ 40.3 in
Therefore, the length of d is approximately 40.3 inches.
Use the image to answer the question.
An illustration shows a square pyramid with labeled parts. The left, front, and right faces of the pyramid and base are visible. The back face is not visible, but its position is indicated by a dashed line. The back base edge is not visible, but its position is indicated by a dashed line. The left base edge is labeled a. The back left lateral edge is labeled e. A dotted line extends from the interior of the vertex straight down to the center of the base and is labeled h. A right angle is indicated where the dotted height line meets the base. Another dotted line extends from the center of the base where the height line meets to the center of the right base edge and is labeled r. A dotted line extends from the right base edge straight up the center of the right face of the prism and meets the height line at the vertex. The dotted slant height line is labeled s.
For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
.
The height of the square pyramid is how many inches?