Two nearby trees are perpendicular to the ground, which is flat. One of these trees is 10 feet tall and

Question

Two nearby trees are perpendicular to the ground, which is flat. One of these trees is $10$ feet tall and has a shadow that is $5$ feet long. At the same time, the shadow of the other tree is $2$ feet long. How tall, in feet, is the other tree?

A.

$3$

B.

$4$

C.

$8$

D.

$27$

Accepted Answer

Choice B is correct. Each tree and its shadow can be modeled using a right triangle, where the height of the tree and the length of its shadow are the legs of the triangle. At a given point in time, the right triangles formed by two nearby trees and their respective shadows will be similar. Therefore, if the height of the other tree is x , in feet, the value of x can be calculated by solving the proportional relationship 10 &#160; feet&#160;tall 5 &#160; feet&#160;long = x &#160; feet&#160;tall 2 &#160; feet&#160;long . This equation is equivalent to 10 5 = x 2 , or 2 = x 2 . Multiplying each side of the equation 2 = x 2 by 2 yields 4 = x . Therefore, the other tree is 4 &#160; feet tall. Choice A is incorrect and may result from calculating the difference between the lengths of the shadows, rather than the height of the other tree. Choice C is incorrect and may result from calculating the difference between the height of the 10 -foot-tall tree and the length of the shadow of the other tree, rather than calculating the height of the other tree. Choice D is incorrect and may result from a conceptual or calculation error.

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