A rectangular prism has a base of 18 cm by 15 cm and a
diagonal of 25 cm . Identify its height. Round to the nearest
tenth.

Question

A rectangular prism has a base of 18 cm by 15 cm and a diagonal of 25 cm . Identify its height. Round to the nearest tenth.

UpStudy AI · Accepted Answer

1. The formula for the space diagonal $$ d $$ of a rectangular prism with length $$ l $$, width $$ w $$, and height $$ h $$ is given by:
   $$
   d = \sqrt{l^2 + w^2 + h^2}
   $$

2. Given $$ l = 18 $$ cm, $$ w = 15 $$ cm, and $$ d = 25 $$ cm, substitute these values into the formula:
   $$
   25 = \sqrt{18^2 + 15^2 + h^2}
   $$

3. Square both sides to remove the square root:
   $$
   25^2 = 18^2 + 15^2 + h^2
   $$
   $$
   625 = 324 + 225 + h^2
   $$

4. Simplify and solve for $$ h^2 $$:
   $$
   324 + 225 = 549
   $$
   $$
   625 = 549 + h^2
   $$
   $$
   h^2 = 625 - 549 = 76
   $$

5. Take the square root of both sides to find $$ h $$:
   $$
   h = \sqrt{76}
   $$

6. Calculate the numerical value and round to the nearest tenth:
   $$
   \sqrt{76} \approx 8.7 \text{ cm}
   $$

Thus, the height of the rectangular prism is approximately $$ 8.7 $$ cm.
The height of the rectangular prism is approximately 8.7 cm.

A rectangular prism has a base of 18 cm by 15 cm and a
diagonal of 25 cm . Identify its height. Round to the nearest
tenth.

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