The height of the taller boy is 100cm.
What is ratio?
Ratio, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.
Let the height of the taller boy be x cm and smaller boy be y cm.
According to the given question.
The ratio of height of the two boys is 4:5.
Since, it is obvious that 4:5 is the ratio of the height of smaller boy to the taller boy. Because k will be the ratio of proportionality then 4k will given the smaller value and 5k will give the larger value therefore, 4:5 represents the ratio of height of smaller boy to the taller boy.
[tex]\implies \frac{y}{x} =\frac{4}{5}[/tex]
Also, the height of the shorter boy is 80cm.
Therefore,
[tex]\frac{80}{x} = \frac{4}{5}[/tex]
[tex]\implies 80\times 5 = 4\times x[/tex]
[tex]\implies 400 = 4\times x[/tex]
[tex]\implies x = \frac{400}{4}[/tex]
[tex]\implies x = 100cm[/tex]
Hence, the height of the taller boy is 100cm.
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