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)
in.
To find the length of d, we can use the Pythagorean theorem.
We know that the length of the front base edge l is 30 in, and the length of the right base edge w is 20 in. So, the length of the hypotenuse of the base triangle is the square root of (30^2 + 20^2) = 36.1 in, which is given as x.
Therefore, the length of d is also 36.1 inches.
To find the length of d, we can use the Pythagorean theorem, which 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 lengths of the other two sides.
In this case, d is the hypotenuse, and x and h are the other two sides of the right-angled triangle.
The equation would be: d^2 = x^2 + h^2
Substituting in the given values: d^2 = 36.1^2 + 18^2
Calculating: d^2 = 1303.21 + 324 = 1627.21
Taking the square root of both sides to find d: d ≈ √1627.21 ≈ 40.3 inches.
Therefore, the length of d is approximately 40.3 inches.
To find the length of d, we can use the concept of Pythagorean theorem.
In the given diagram, we can see that d is the hypotenuse of a right triangle formed by x, l, and d.
According to Pythagorean theorem, in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
Therefore, we have the equation:
x^2 + l^2 = d^2
Substituting the given values, we get:
(36.1)^2 + (30)^2 = d^2
Simplifying the equation:
1303.21 + 900 = d^2
2203.21 = d^2
Taking square root on both sides to solve for d:
d = √(2203.21)
Calculating the square root:
d ≈ 46.9 in.
So, the length of d is approximately 46.9 inches.