Answer:
10 units.
Step-by-step explanation:
Given:
- [tex]\text{Volume of prism = 2500 units}^{3}[/tex]
- [tex]\text{Length: 25 units}[/tex]
- [tex]\text{Width: 10 units}[/tex]
Formula:
[tex]\text{Volume of rectangular prism = Length} \times \text{Width} \times \text{Height}[/tex]
Substitute the length, width, and the volume of the prism in the formula
[tex]\implies \text{2500 = 25} \times 10 \times \text{Height}[/tex]
Divide 25 × 10 to both sides of the equation to isolate "Height"
[tex]\implies \dfrac{\text{2500}}{25 \times 10} = \dfrac{25 \times 10 \times \text{Height}}{25\times 10}[/tex]
[tex]\implies \dfrac{\text{2500}}{25 \times 10} = \text{Height}[/tex]
Simplify the left hand side of the equation
[tex]\implies \dfrac{{25 \times 10 \times 10}}{25 \times 10} = \text{Height} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [2500 =25 \times 10 \times 10][/tex]
[tex]\implies \dfrac{{10}}{1} = 10 = \text{Height}[/tex]
Therefore, the measure of the height is 10 units.
