Question

two arcs of the same circle have their lengths in the ratio 4:5. Find the ratio of the areas of the corresponding
sectors.​

Answer 1

Ratio of the areas of the corresponding sectors will be 4:5

Step-by-step explanation:

Ratio of the lengths of two arcs of the same circle = 4:5

Then the lengths of two arcs = 4x and 5x

Let the length of two arcs are a, b and area of the corresponding sectors are A and A'.

Let the lengths of two arcs are l and l'

Then l = 4x and l' = 5x

Now area of the corresponding sectors A = $\frac{rl}{2}$  and A' = $\frac{rl'}{2}$

Now $\frac{A}{A'}=\frac{\frac{rl}{2}}{\frac{rl'}{2}}$

$\frac{A}{A'}=\frac{l}{l'}$

$\frac{A}{A'}=\frac{4x}{5x}$

$\frac{A}{A'}=\frac{4}{5}$

Therefore, ratio of the corresponding sectors will be 4:5

Learn more about the area of the sector in a circle from https://brainly.in/question/3090029

Answer 2

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