Question

The football coach is overseeing the installation of new goal posts on the football field. He is wondering if the goal posts are at the regulation height, which is 20 feet, measured from the ground to the top of the post. One afternoon, the coach, who is 6 feet tall, measured his own shadow at 4 feet long. He measured the shadow of the goal post as 12 feet long. Is the goal post at the regulation height?
A. Yes, since the ratios of the corresponding sides are proportional.
B. Yes, since the ratios of the corresponding sides are congruent.
C. Not enough information is given.
D. No, since the ratios of the corresponding sides are not proportional.

Answer 1

Answer:

Correct option is D. No, since the ratios of the corresponding sides are not proportional.

Step-by-step explanation:

Please refer to the attached figure

Let height of coach represents by AB = 6 feet

And shadow of coach represents by BC = 4 feet

Let height of goal post represents by DE = x feet

And Shadow of goal post represents by EF = 12 feet.

Since measurement of shadows are at same time. therefore  ratio of height of coach and height of goal post  must be same as ratio of shadow of coach and shadow of goal post.

⇒ 6/x = 4/12

⇒x = 72/4 = 18 feet

So goal post is not at regular height , since expected height is 20 feet while actual height is 18 feet . And if we consider value of x as 20 feet instead of 18 feet , ratio of corresponding sides will not match.

Hence correct answer is D. No, since the ratios of the corresponding sides are not proportional.