Answer:
18 mm
Step-by-step explanation:
We can see that △RVW and △RST are similar because they have the same angle measures.
This means that the ratios of their side lengths are equal. We can use this information to create an equation to solve for D:
[tex]\dfrac{\text{bottom side of }\triangle RVW}{\text{left side of }\triangle RVW} =\dfrac{\text{bottom side of }\triangle RST}{\text{left side of }\triangle RST}[/tex]
↓↓↓ plugging in the given side lengths
[tex]\dfrac{D}{15} = \dfrac{24}{15 + 5}[/tex]
↓ simplifying the denominator on the right side
[tex]\dfrac{D}{15} = \dfrac{24}{20}[/tex]
↓ cross-multiplying
[tex]20D = 24 \cdot 15[/tex]
↓ dividing both sides by 20
[tex]D = \dfrac{24\cdot 15}{20}[/tex]
↓ simplifying the fraction
[tex]\boxed{D = 18\text{ mm}}[/tex]
