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Question 1 of 17, Step 1 of 10/21CorrectBill uses mirrors to augment the "laser experience" at a laser show. At one show he places threemirrors, A, B, C, in a right triangular form. If the distance between A and B is 9 m more than thedistance between A and C, and the distance between B and C is 9 m less than the distance between Aand C, what is the distance between mirror A and mirror C?

Sagot :

The given situation can be illustrated as follow:

The blue lines represent the mirrors.

Based on the given information you have:

AB = 9 + AC

BC = AC - 9

By using the Pythagorean theorem you can write:

[tex](AB)^2=(BC)^2+(AC)^2[/tex]

Replace the given expressions for AB and BC into the previous equation and solve for AC, as follow:

[tex]\begin{gathered} (9+AC)^2=(AC-9)^2+(AC)^2 \\ 81+2\cdot9\cdot AC+(AC)^2=(AC)^2-2\cdot9(AC)+81+(AC)^2 \\ 18AC+18AC=(AC)^2 \\ 36AC=(AC)^2 \end{gathered}[/tex]

Where we have expanaded (9+AC)^2 and (AC-9)^2. By dividing by AC both sides:

[tex]\begin{gathered} 36=AC \\ AC=36 \end{gathered}[/tex]

Hence, the distance between mirrors A and C is 36

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