Mathematics, 25.03.2020 00:05 lrg34

I NEED HELP WILL GIVE BRAINLIEST

A rectangular box is 8 inches in length, 3 inches in width, and 5 inches in height.

A. Suppose the three-dimensional diagonal is also the hypotenuse of a right triangle. If a vertical edge is one of the legs of that right triangle, what is the length of the second leg? Round your answer to the nearest tenth of an inch. Show all of your work.

B. Determine the length of the three-dimensional diagonal. Round your answer to the nearest tenth of an inch. Show all of your work.

I NEED HELP WILL GIVE BRAINLIEST A rectangular box is 8 inches in length, 3 inches in width, and 5 i

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Answer from: SKYBLUE1015

A. The length of the second leg is 8.5 inches

B. The length of the three-dimensional diagonal is 9.9 inches

Step-by-step explanation:

Let us revise the relation between the hypotenuse and the two legs of a right triangle

(hypotenuse)² = (vertical leg)² + (horizontal leg)²

∵ The length of the rectangular box = 8 inches

∵ The width of the rectangular box = 3 inches

∵ The height of the rectangular box = 5 inches

∵ Length and width are perpendicular to each other

∴ The Δ whose legs are 3 and 8 is a right triangle

In the right Δ whose legs are 3 and 8

∵ (hypotenuse)² = (3)² + (8)²

∴ (hypotenuse)² = 9 + 64

∴ (hypotenuse)² = 73

- Take √ for both sides

∴ hypotenuse = $\sqrt{73}$ = 8.544003745

- Round it to the nearest tenth of one inch

∴ hypotenuse = 8.5 inches

The 3-dimensional diagonal is the hypotenuse of a right triangle whose legs are the vertical edge and the hypotenuse of the right triangle whose legs are 3 and 8

∵ The hypotenuse of the right triangle whose legs are 3 and

8 is 8.5 inches

∴ The length of the second leg is 8.5 inches

In the right triangle whose hypotenuse is the 3-dimensional diagonal and legs are the vertical edge , the hypotenuse of the right triangle whose legs are 3 and 8

∵ (3-dimensional diagonal)² = (5)² + (73)²

∴ (3-dimensional diagonal)² = 25 + 73

∴ (3-dimensional diagonal)² = 98

- Take √ for both sides

∴ 3-dimensional diagonal = $\sqrt{98}$ = 9.899494937

- Round it to the nearest tenth of an inch

∴ 3-dimensional diagonal = 9.9 inches

∴ The length of the three-dimensional diagonal is 9.9 inches

V.I.N: you can find the length of the three-dimensional diagonal by using this rule → $d=\sqrt{l^{2}+w^{2}+h^{2}}$

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