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.
To find the length of d, we need to use the formula for the diagonal of a rectangular prism, which is given by:
d = √(l^2 + w^2 + h^2)
Plugging in the values given:
d = √(30^2 + 20^2 + 18^2)
d = √(900 + 400 + 324)
d = √(1624)
Using a calculator, we find that √(1624) ≈ 40.3 inches.
Therefore, the length of d is approximately 40.3 inches.
To find the length of d, we can use the Pythagorean theorem. The formula is:
a^2 + b^2 = c^2
In this case, the two sides of the right triangle formed by l, w, and d are l and w, and the hypotenuse is d. Therefore, the equation becomes:
l^2 + w^2 = d^2
Plugging in the values, we have:
30^2 + 20^2 = d^2
Simplifying, we get:
900 + 400 = d^2
1300 = d^2
To solve for d, we take the square root of both sides of the equation:
d = √1300
Using a calculator, we find that √1300 is approximately 36.06.
Rounding to the nearest tenth, the length of d is 36.1 inches.
To find the length of d, we need to make use of the Pythagorean theorem. The Pythagorean theorem 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 other two sides.
In this case, the triangle formed by the dimensions l, w, and d is a right-angled triangle. The sides l and w are the known dimensions, while d is the unknown. The equation we can set up using the Pythagorean theorem is:
l^2 + w^2 = d^2
Substituting the known values:
(30 in)^2 + (20 in)^2 = d^2
900 in^2 + 400 in^2 = d^2
1300 in^2 = d^2
To solve for d, we need to find the square root of 1300 in^2:
d = sqrt(1300 in^2)
Using a calculator, we find:
d ≈ 36.06 in
Rounding to the nearest tenth, the length of d is approximately 36.1 in.