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Travka [436]
3 years ago
13

A 6-ft tall football player casts a 16-in. shadow. at the same time, the stadium bleachers cast a 6-ft shadow. how tall are the

bleachers?
Mathematics
1 answer:
spin [16.1K]3 years ago
4 0
You need to use a ratio of height (H) to shadow length (L) to solve the first problem. It's basically a use of similar triangles, with two perpendicular sides, and with the shadow making the same angle with the vertical. 

<span>6 ft = 72 ins, so that rH/L = 72/16 = 9/2 for the player. </span>

<span>So the bleachers are 9/2 x 6 ft = 27 ft. </span>

<span>For the second problem, 9 ft = 108 in, so that the ratio of the actual linear dimensions to the plan's linear dimensions are 9ft/(1/2in) = 2 x 108 = 216. </span>

<span>So the stage will have dimensions 216 times larger than 1.75" by 3". </span>

<span>That would be 31ft 6ins x 54ft. </span>
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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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  5. Division
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Step-by-step explanation:

<u>Step 1: Define Systems</u>

y = -x + 1

2x + 3y = 6

<u>Step 2: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

  1. Substitute in <em>y</em>:                    2x + 3(-x + 1) = 6
  2. Distribute 3:                         2x - 3x + 3 = 6
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  5. Isolate <em>x</em>:                              x = -3

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  4. Add:                                         y = 4
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