16. By the age of 11, a boy has reached 81\% of his full height, while a girl has reached 88\% of her full height. If both are 140 cm tall at this age, who is likely to be taller as adults and by how much?
Key Concept: Growth Rate Comparison
a) The boy by 13.8 cm
[Solution Description]
First, we calculate the full height of the boy using the formula:
$\text{Full height}_{\text{boy}} = \frac{\text{Present height}}{\% \text{ of full height}} \times 100 = \frac{140}{81} \times 100$
Calculating this:
$\text{Full height}_{\text{boy}} = 172.84 \text{ cm}$
Next, we calculate the full height of the girl:
$\text{Full height}_{\text{girl}} = \frac{\text{Present height}}{\% \text{ of full height}} \times 100 = \frac{140}{88} \times 100$
Calculating this:
$\text{Full height}_{\text{girl}} = 159.09 \text{ cm}$
The boy is likely to be taller as an adult. The difference in their full heights is:
$172.84 - 159.09 = 13.75 \text{ cm}$
Therefore, the boy is likely to be approximately 13.8 cm taller than the girl.
Your Answer is correct.
a) The boy by 13.8 cm
[Solution Description]
First, we calculate the full height of the boy using the formula:
$\text{Full height}_{\text{boy}} = \frac{\text{Present height}}{\% \text{ of full height}} \times 100 = \frac{140}{81} \times 100$
Calculating this:
$\text{Full height}_{\text{boy}} = 172.84 \text{ cm}$
Next, we calculate the full height of the girl:
$\text{Full height}_{\text{girl}} = \frac{\text{Present height}}{\% \text{ of full height}} \times 100 = \frac{140}{88} \times 100$
Calculating this:
$\text{Full height}_{\text{girl}} = 159.09 \text{ cm}$
The boy is likely to be taller as an adult. The difference in their full heights is:
$172.84 - 159.09 = 13.75 \text{ cm}$
Therefore, the boy is likely to be approximately 13.8 cm taller than the girl.