A boy who is 3 feet tall can cast a shadow on the ground that is 7 feet long. How tall is a man who can cast a shadow that is 14 feet long? Solve this problem by setting up a proportion. Show your work.

since the boy's shadow is 7 feet, and the mans shadow is 14 feet, the proportion of the boy to the man is 7/14, or 1/2
1/2= 3/x
x/2=3 (multiply both sides by x)
x=6 (multiply both sides by 2)
The Mans height is 6 feet

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bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-01-14T06:23:41+01:00

Proportion is a method to compare the ratio of the two quantities of the same units. Using the proportion we can compare the part of a whole of a number with other part of the whole. .The height of the man who can cast the 14 feet long shadow on the ground is 6 feet.

Given-

The height of the boy is 3 feet.

The length of the shadow cast by the boy on the ground is 7 feet.

To find the height of the man who can cast the 14 feet long shadow on the ground we need to know about Proportion.

What is proportion?

Proportion is a method to compare the ratio of the two quantities of the same units. Using the proportion we can compare the part of a whole of a number with other part of the whole.

For the given problem as the 3 feet tall boy can cast a shadow on the ground that is 7 feet long. To calculate the shadow cast by the one feet tall boy we need to divide the height of the boy to the shadow made by him on the ground. Thus the shadow cast by the one feet tall boy can be given as,

[tex]=\dfrac{7}{3}[/tex]

Suppose the height of the man who can cast the 14 feet long shadow on the ground is x. For this case the shadow cast by the one feet tall boy can be given as,

[tex]=\dfrac{14}{x}[/tex]

Comparing both the ratios,

[tex]=\dfrac{7}{3}=\dfrac{14}{x}[/tex]

[tex]x=\dfrac{7\times3}{14}[/tex]

[tex]x=6[/tex]

Thus the height of the man who can cast the 14 feet long shadow on the ground is 6 feet.

Learn more about the proportion here;

https://brainly.com/question/2548537