To find the length of the diagonal of the prism, we can use the Pythagorean theorem.
The diagonal is the hypotenuse of a right triangle formed by the length, width, and height of the prism.
Using the formula:
Diagonal = √(Length^2 + Width^2 + Height^2)
We have:
Diagonal = √(12^2 + 3^2 + 4^2)
Diagonal = √(144 + 9 + 16)
Diagonal = √(169)
Diagonal = 13 cm
So, the length of the diagonal of the prism is 13 cm.
12 cm, 3 cm, 4 cm
Find the length of the diagonal of the prism.
__cm
7 answers
The Great Pyramid of Giza in Egypt has a square base with edge length of 230.5 m and a slant height of 180.2 m. Find the height of the pyramid. Round the answer to the nearest tenth
__m
__m
To find the height of the pyramid, we can use the Pythagorean theorem.
The height, slant height, and half the base form a right triangle.
Using the formula:
Height = √(Slant height^2 - (Half base)^2)
We have:
Height = √(180.2^2 - (230.5/2)^2)
Height = √(32544.04 - 26577.25)
Height = √(5966.79)
Height ≈ 77.2 m
Rounding to the nearest tenth, the height of the pyramid is approximately 77.2 m.
The height, slant height, and half the base form a right triangle.
Using the formula:
Height = √(Slant height^2 - (Half base)^2)
We have:
Height = √(180.2^2 - (230.5/2)^2)
Height = √(32544.04 - 26577.25)
Height = √(5966.79)
Height ≈ 77.2 m
Rounding to the nearest tenth, the height of the pyramid is approximately 77.2 m.
Keysha is building a coffee table. It's going to be in the shape of a rectangular prism, without the faces. She wants to make the table decorative by adding metal diagonals. The length of the coffee table will be 44 in., the width 24in., and the height 14 in. Find the length Keysha should make each diagonal. Round the answer to the nearest tenth.
__in.
__in.
To find the length of the diagonal, we can use the Pythagorean theorem.
The diagonal is the hypotenuse of a right triangle formed by the length, width, and height of the coffee table.
Using the formula:
Diagonal = √(Length^2 + Width^2 + Height^2)
We have:
Diagonal = √(44^2 + 24^2 + 14^2)
Diagonal = √(1936 + 576 + 196)
Diagonal = √(2708)
Diagonal ≈ 52.0 in.
Rounding to the nearest tenth, Keysha should make each diagonal approximately 52.0 in. long.
The diagonal is the hypotenuse of a right triangle formed by the length, width, and height of the coffee table.
Using the formula:
Diagonal = √(Length^2 + Width^2 + Height^2)
We have:
Diagonal = √(44^2 + 24^2 + 14^2)
Diagonal = √(1936 + 576 + 196)
Diagonal = √(2708)
Diagonal ≈ 52.0 in.
Rounding to the nearest tenth, Keysha should make each diagonal approximately 52.0 in. long.
a, b, c
a, c, b
b, c, a
b, c, a
Explain a proof of the Pythagorean Theorem using the image.
a, c, b
b, c, a
b, c, a
Explain a proof of the Pythagorean Theorem using the image.
Apologies, but for the Pythagorean Theorem, we need the lengths of the sides of a right triangle, not just the order of the sides. Could you please provide the length of the sides a, b, and c?