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How do you find the height of a rectangular box when length is 7 m and width is 5 m and diagonal length 10m?
I guess the diagonal length given is from one corner of the box to the opposite corner reached by traversing one length side, one edge side and one height side.
Using Pythagoras, the length of the diagonal of the base (length by width) can be found.
Using this diagonal and the height of the box, the diagonal from corner-to-opposite-corner of the box can be found using Pythagoras. However, as this [longer] diagonal is know, the height can be found by rearranging this last use of Pythagoras:
Diagonal_base2 = length2 + width2
Diagonal_box2 = diagonal_base2 + height2
⇒ height = √(diagonal_box2 - diagonal_base2 )
= √(diagonal_box2 - (length2 + width2))
= √(diagonal_box2 - length2 - width2)
Now that the formula has been derived, plugging in (substituting) the various lengths will allow the height to be calculated.
What else can I help you with?
What is the formula for calculating the length of the space diagonal of a right rectangular prism on the basis of the prism's length l width w and height h?
The formula for calculating the length of the space diagonal ( d ) of a right rectangular prism is given by the equation ( d = \sqrt{l^2 + w^2 + h^2} ), where ( l ) is the length, ( w ) is the width, and ( h ) is the height of the prism. This formula derives from the Pythagorean theorem, applied in three dimensions.
How do you find the volume to a rectangular prism?
Volume of a rectangular prism is length x height x width.
What is the surface volume of a rectangular prism with a length of 11m width of 8m and height of 3m?
A rectangular prism with a length of 11m, width of 8m and height of 3m has a volume of 264m3
What is the volume of a rectangular prism with a height of 7 a width of 5 and a length of 8?
A rectangular prism with a height of 7, a width of 5 and a length of 8 has a volume of 280 units3
What is the formula for calculating the length of the space diagonal of a right rectangular prism on the basis of the prisms length width and height?
It is the extension of Pythagoras's theorem to 3-d. d2 = l2 + w2 + h2
What are three dimensions are needed to find the volume of a rectangular solid?
length, width, height
What is the formula for calculating the length of the space diagonal of a right rectangular prism on the basis of the prism's length l width w and height h?
The formula for calculating the length of the space diagonal ( d ) of a right rectangular prism is given by the equation ( d = \sqrt{l^2 + w^2 + h^2} ), where ( l ) is the length, ( w ) is the width, and ( h ) is the height of the prism. This formula derives from the Pythagorean theorem, applied in three dimensions.
What is the formula for calculating the length of the diagonal of a right rectangular prism on the basis of the prisms length width and height?
It is an extension of Pythagoras's theorem to 3-dimensions. Diagonal2 = Length2 + Width2 + Height2
What is the volume of the rectangular prism with length l width w and height h?
The volume of a rectangular prism is given by the formula volume of rectangular prism = length x width x height If the length is l, the width is w and the height is h the volume is given by volume = lwh
How do you find the volume to a rectangular prism?
Volume of a rectangular prism is length x height x width.
How does the volume of a rectangular prism change the length is doubled?
The volume of a rectangular prism is calculated by multiplying its length, width, and height (V = length × width × height). If the length is doubled while keeping the width and height the same, the new volume becomes V = (2 × length) × width × height, effectively doubling the original volume. Thus, the volume of the rectangular prism increases by a factor of two when the length is doubled.
What is the surface volume of a rectangular prism with a length of 11m width of 8m and height of 3m?
A rectangular prism with a length of 11m, width of 8m and height of 3m has a volume of 264m3
What is the volume of a rectangular prism with a height of 7 a width of 5 and a length of 8?
A rectangular prism with a height of 7, a width of 5 and a length of 8 has a volume of 280 units3
What is the formula for calculating the length of the space diagonal of a right rectangular prism on the basis of the prisms length width and height?
It is the extension of Pythagoras's theorem to 3-d. d2 = l2 + w2 + h2
What form of measurement is measuring length width and height?
The measurement of length, width, and height finds the volume of a cube or rectangular prism.
How do you find the height of a rectangular prism if the volume is 455 the length is 10 and the width is 7?
Volume = Length x Width x Height So Height = Volume / (Length x Width)
Is it true that multiplying length width height finds the volume of a rectangular object?
Yes, it is true. Multiplying the length, width, and height of a rectangular object calculates its volume. The formula is expressed as Volume = length × width × height, which gives the amount of space the object occupies. This applies to rectangular prisms and similar shapes.
