A cube is made up of six congruent square faces. Find the length of the inner diagonal of the cube. Note that is the hypotenuse of right triangle ADH. (Round your answer to the nearest hundredth.)

a. Use the 45-45-90 property or the Pythagorean Theorem to find the length of the diagonal (DH) of the bottom base of the cube.

b. Use the length from part a as one leg, the length of side AD, and the Pythagorean Theorem to find the length of the diagonal AH.

Question

Mathematics

Romeo Daniel

14 January, 14:47

A cube is made up of six congruent square faces. Find the length of the inner diagonal of the cube. Note that is the hypotenuse of right triangle ADH. (Round your answer to the nearest hundredth.)

a. Use the 45-45-90 property or the Pythagorean Theorem to find the length of the diagonal (DH) of the bottom base of the cube.

b. Use the length from part a as one leg, the length of side AD, and the Pythagorean Theorem to find the length of the diagonal AH.

+1

Answers (1)

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Jackson Houston · Answer 1

A) The 45-45-90 property states that the hypotenuse is root2 times the length of either leg. That means that the diagonal (DH) is root2 the length of one side.

b) The inner diagonal is not a 45-45-90. That means you have to use pythagorean theorem, or a^2+b^2=c^2. (root2 length) ^2 + (length) ^2 = c^2

c would be root 3 length