1 answer:
Answer/Step-by-step explanation:
The two triangles we have in the diagram shar the same vertex. They are both similar triangles. Therefore, their side lengths would be proportional.
This means:
![\frac{9.8}{4.3} = \frac{r}{5.1} = \frac{n}{2.7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B9.8%7D%7B4.3%7D%20%3D%20%5Cfrac%7Br%7D%7B5.1%7D%20%3D%20%5Cfrac%7Bn%7D%7B2.7%7D%20)
Solve for variable r and n respectively.
Thus:
![\frac{9.8}{4.3} = \frac{r}{5.1}](https://tex.z-dn.net/?f=%20%5Cfrac%7B9.8%7D%7B4.3%7D%20%3D%20%5Cfrac%7Br%7D%7B5.1%7D%20)
Multiply both besides by 5.1
![\frac{9.8}{4.3} \times 5.1 = \frac{r}{5.1} \times 5.1](https://tex.z-dn.net/?f=%20%5Cfrac%7B9.8%7D%7B4.3%7D%20%5Ctimes%205.1%20%3D%20%5Cfrac%7Br%7D%7B5.1%7D%20%5Ctimes%205.1%20)
![\frac{9.8 \times 5.1}{4.3} = r](https://tex.z-dn.net/?f=%20%5Cfrac%7B9.8%20%5Ctimes%205.1%7D%7B4.3%7D%20%3D%20r%20)
11.6 = r (nearest tenth)
Also,
![\frac{9.8}{4.3} = \frac{n}{2.7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B9.8%7D%7B4.3%7D%20%3D%20%5Cfrac%7Bn%7D%7B2.7%7D%20)
Multiply both besides by 2.7
![\frac{9.8}{4.3} \times 2.7 = \frac{n}{5.1} \times 2.7](https://tex.z-dn.net/?f=%20%5Cfrac%7B9.8%7D%7B4.3%7D%20%5Ctimes%202.7%20%3D%20%5Cfrac%7Bn%7D%7B5.1%7D%20%5Ctimes%202.7%20)
![\frac{9.8 \times 2.7}{4.3} = r](https://tex.z-dn.net/?f=%20%5Cfrac%7B9.8%20%5Ctimes%202.7%7D%7B4.3%7D%20%3D%20r%20)
6.2 = n (nearest tenth)
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Answer:
Step-by-step explanation:
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