Using wooden rulers, classmates make the following measurements and calculate ratios.
Alara measures the width of her head to be \(12\) cm. She then measures the width of her eye to be \(2.4\) cm. What is the ratio of the width of her head to the width of her eye?
Romaisa measures the height of her head to be \(20\) cm. She then measures her total height to be \(1.4\) m. What is the ratio of the height of her head to her total height?
Brody measures the length of his nose to be \(5\) cm. If the ratio of the length of his nose to the length of his index finger is \(2:3\), then what is the length of his index finger, in centimetres?
Using wooden rulers, calculate the measurements from parts (a), (b), and (c) yourself. Are your ratios similar?
Since \(12 = 5\times 2.4\), the ratio of the width of her head to the width of her eye is \(5:1.\)
We first convert \(1.4\) m to cm. Since there are \(100\) cm in \(1\) m, we have \(1.4 \text{ m} = 140 \text{ cm}.\)
Since \(140 = 7 \times 20\), the ratio of the height of her head to her total height is \(1:7.\)
The ratio of the length of his nose to the length of his index finger is \(2:3.\) The ratio \(2:3\) means that for every \(2\) parts of the nose, the index finger has \(3\) parts. Since \(2\) parts of the nose is \(5\) cm, this means \(1\) part is equal to \(5 \div 2 = 2.5\) cm. The index finger corresponds to \(3\) parts, so we multiply \(2.5\) by \(3.\) This gives the length of the index finger as \(3 \times 2.5 = 7.5\) cm.
Thus, if the length of his nose is \(5\) cm, the length of his index finger is \(7.5\) cm.
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