Respuesta :
Answer:
The ratio of the radius of the smaller watch face to the radius of the larger watch face is 4:5.
Step-by-step explanation:
Let the Area of smaller watch face be [tex]A_1[/tex]
Also Let the Area of Larger watch face be [tex]A_2[/tex]
Also Let the radius of smaller watch face be [tex]r_1[/tex]
Also Let the radius of Larger watch face be [tex]r_2[/tex]
Now given:
[tex]\frac{A_1}{A_2} =\frac{16}{25}[/tex]
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;
[tex]A_1 = \pi {r_1}^2[/tex]
[tex]A_2 = \pi {r_2}^2[/tex]
So we get;
[tex]\frac{A_1}{A_2}= \frac{\pi {r_1}^2}{\pi {r_2}^2}[/tex]
Substituting the value we get;
[tex]\frac{16}{25}= \frac{\pi {r_1}^2}{\pi {r_2}^2}[/tex]
Now 'π' from numerator and denominator gets cancelled.
[tex]\frac{16}{25}= \frac{{r_1}^2}{{r_2}^2}[/tex]
Now Taking square roots on both side we get;
[tex]\sqrt{\frac{16}{25}}= \sqrt{\frac{{r_1}^2}{{r_2}^2}}\\\\\frac{4}{5}= \frac{r_1}{r_2}[/tex]
Hence the ratio of the radius of the smaller watch face to the radius of the larger watch face is 4:5.
