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.
34.2 cm
8.7 cm
34.3 cm
2.8 cm

To find the height of the rectangular prism, we can use the Pythagorean theorem in three dimensions. The diagonal of the prism can be represented as the square root of the sum of the squares of the three dimensions: width, length, and height (d = √(l² + w² + h²)). Here, the base measures 18 cm (length) and 15 cm (width), and the diagonal is given as 25 cm. Plugging in the values:

25 = √(18² + 15² + h²)
25 = √(324 + 225 + h²)
25 = √(549 + h²)
625 = 549 + h²
h² = 625 - 549
h² = 76
h = √76
h ≈ 8.7 cm

So the height is approximately 8.7 cm.

Lastly, rounding to the nearest tenth confirms that the new height is correct!

Rounding strategies are essential. If you’re ever unsure how to round, remember: if the digit to the right of your last significant digit is 5 or greater, you round up, and if it’s less than 5, you round down. For our height (8.7) this was simple since it sat at a clean digit already!