Given I=30in, w=20in, h=18in, and x=36.1in. Find the length of d. round the answer to the nearest tenth
To find the length of d, we can use the formula for the diagonal of a rectangular prism. The formula is:
d = √(w^2 + h^2 + x^2)
Given:
w = 20in
h = 18in
x = 36.1in
Substituting the given values into the formula, we have:
d = √(20^2 + 18^2 + 36.1^2)
Now, let's calculate this:
d = √(400 + 324 + 1303.21)
d = √(2027.21)
d ≈ 45.03
Rounding the answer to the nearest tenth, the length of d is approximately 45.0 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 is equal to the sum of the squares of the lengths of the other two sides.
The given dimensions do not specify which sides are the legs and which is the hypotenuse. Therefore, we can consider all three cases and take the maximum value obtained.
Case 1: I and w are the legs, and d is the hypotenuse.
Using the Pythagorean theorem, we have:
d^2 = I^2 + w^2
d^2 = (30in)^2 + (20in)^2
d^2 = 900in^2 + 400in^2
d^2 = 1300in^2
d ≈ 36.06in
Case 2: I and h are the legs, and d is the hypotenuse.
Using the Pythagorean theorem, we have:
d^2 = I^2 + h^2
d^2 = (30in)^2 + (18in)^2
d^2 = 900in^2 + 324in^2
d^2 = 1224in^2
d ≈ 35.00in
Case 3: w and h are the legs, and d is the hypotenuse.
Using the Pythagorean theorem, we have:
d^2 = w^2 + h^2
d^2 = (20in)^2 + (18in)^2
d^2 = 400in^2 + 324in^2
d^2 = 724in^2
d ≈ 26.93in
Taking the maximum value obtained, we have d ≈ 36.06in.
To find the length of d, we can use the formula for the diagonal of a rectangular prism, which is given by:
d = √(w^2 + h^2 + x^2)
Substituting the given values, we have:
d = √(20^2 + 18^2 + 36.1^2)
d = √(400 + 324 + 1303.21)
d = √(2027.21)
d ≈ 45.0 inches (rounded to the nearest tenth)
Therefore, the length of d is approximately 45.0 inches.