Final answer:
To solve the equations, set up proportions by setting each ratio equal to the unit scale. Cross-multiply and solve for the unknowns to find the length and width ratios.
Step-by-step explanation:
To solve the given equations, we need to set up proportions by setting each ratio equal to the unit scale. Let's go through each equation:
a) 3/4 = 6/8
To form a proportion, we set the length ratios equal to each other:
3/4 = L/1
Cross-multiplication gives us 4L = 3*1, which simplifies to 4L = 3. Dividing both sides by 4, we find L = 3/4.
For the width ratios, we have:
6/8 = W/1
Cross-multiplication gives us 8W = 6*1, which simplifies to 8W = 6. Dividing both sides by 8, we find W = 6/8.
b) 5/2 = 15/6
Again, we set the length ratios equal to each other:
5/2 = L/1
Cross-multiplication gives us 2L = 5*1, which simplifies to 2L = 5. Dividing both sides by 2, we find L = 5/2.
For the width ratios, we have:
15/6 = W/1
Cross-multiplication gives us 6W = 15*1, which simplifies to 6W = 15. Dividing both sides by 6, we find W = 15/6.
c) 1/3 = 2/6
Setting the length ratios equal to each other:
1/3 = L/1
Cross-multiplication gives us 3L = 1*1, which simplifies to 3L = 1. Dividing both sides by 3, we find L = 1/3.
For the width ratios, we have:
2/6 = W/1
Cross-multiplication gives us 6W = 2*1, which simplifies to 6W = 2. Dividing both sides by 6, we find W = 2/6.
d) 7/8 = 14/16
Setting the length ratios equal to each other:
7/8 = L/1
Cross-multiplication gives us 8L = 7*1, which simplifies to 8L = 7. Dividing both sides by 8, we find L = 7/8.
For the width ratios, we have:
14/16 = W/1
Cross-multiplication gives us 16W = 14*1, which simplifies to 16W = 14. Dividing both sides by 16, we find W = 14/16.