Question

ASAP PLEASE HELP

In the rectangular prism below. RV=29. RS = 21. and RT= 24. Find the length of the diagonal RU.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.

Answer 1

The length of the diagonal of the box is approximately 31 units.

Diagonal of a Box

Diagonal, d, = √(length² + width² + height²)

Given:

RV=29

RS = 21

RT= 24

Thus:

length of the box = ST = ?

Use Pythagorean Theorem to find ST:

ST = √(RT² - RS²)

Substitute

ST = √(24² - 21²)

ST = 12

Height of the box = SV = ?

Use Pythagorean Theorem to find SV:

SV = √(RV² - RS²)

Substitute

SV = √(29² - 21²)

SV = 20

Find the diagonal of the box, RU:

RU = √(ST² + RS² + SV²)

Substitute

RU = √(12² + 21² + 20²)

RU = 31 units.

Therefore, the length of the diagonal of the box is approximately 31 units.

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