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allsm [11]
3 years ago
9

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 o

f the larger watch face?
Mathematics
1 answer:
Leona [35]3 years ago
7 0

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 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:

\frac{A_1}{A_2} =\frac{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;

\frac{A_1}{A_2}= \frac{\pi {r_1}^2}{\pi {r_2}^2}

Substituting the value we get;

\frac{16}{25}= \frac{\pi {r_1}^2}{\pi {r_2}^2}

Now 'π' from numerator and denominator gets cancelled.

\frac{16}{25}= \frac{{r_1}^2}{{r_2}^2}

Now Taking square roots on both side we get;

\sqrt{\frac{16}{25}}= \sqrt{\frac{{r_1}^2}{{r_2}^2}}\\\\\frac{4}{5}= \frac{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.

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