Answered: "The areas of the two watch faces have..."

Layne Massey

Answered question

2022-02-11

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? What is the radius of the larger watch face?

Iacopelli5co

Beginner2022-02-12Added 15 answers

Step 1

A_{1} : A_{2} = 16 : 25

A = π r^{2}

\Rightarrow π r_{1}^{2} : π r_{2}^{2} = 16 : 25

\Rightarrow \frac{π r_{1}^{2}}{π r_{2}^{2}} = \frac{16}{25}

\Rightarrow \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{4^{2}}{5^{2}}

\Rightarrow \frac{r_{1}}{r_{2}} = \frac{4}{5}

\Rightarrow r_{1} : r_{2} = 4 : 5

\Rightarrow r_{2} = 5

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