Question

The areas of the two watch faces have a ratio of 16:25 What is the ratio of the radius of the smaller watch face to the radius of the larger watch face?

Answer 1

The ratio of the radius of the smaller watch face to the radius of the larger watch face is 4:5.

Explanation:

Let the Area of smaller watch face be
`A_1`

Also Let the Area of Larger watch face be
`A_2`

Also Let the radius of smaller watch face be
`r_1`

Also Let the radius of Larger watch face be
`r_2`

Now given:

`(A_1)/(A_2) =(16)/(25)`

We need to find the ratio of the radius of the smaller watch face to the radius of the larger watch face.

Solution:

Since the watch face is in circular form.

Then we can say that;

Area of the circle is equal 'π' times square of the radius 'r'.

framing in equation form we get;

`A_1 = \pi {r_1}^2`

`A_2 = \pi {r_2}^2`

So we get;

`(A_1)/(A_2)= \frac{\pi {r_1}^2}{\pi {r_2}^2}`

Substituting the value we get;

`(16)/(25)= \frac{\pi {r_1}^2}{\pi {r_2}^2}`

Now 'π' from numerator and denominator gets cancelled.

`(16)/(25)= \frac{{r_1}^2}{{r_2}^2}`

Now Taking square roots on both side we get;

`\sqrt{(16)/(25)}= \sqrt{\frac{{r_1}^2}{{r_2}^2}}\\\\(4)/(5)= (r_1)/(r_2)`

Hence the ratio of the radius of the smaller watch face to the radius of the larger watch face is 4:5.