Answer:
x = 2.5
Step-by-step explanation:
It is given based on the topic that these are similar right triangles. Note the placement of the right angles. The 2 and x are base, while the 7.5 and 6 are hypotenuses. There are a couple of ways you can set the equation, but in this case I will set it as [tex]\frac{base}{hypotenuse}[/tex]
Set the equation:
[tex]\frac{2}{6} = \frac{x}{7.5}[/tex]
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Multiply 6 and 7.5 to both sides of the equation:
[tex]7.5 * 6 * (\frac{2}{6}) = (\frac{x}{7.5}) * 6 * 7.5\\7.5 * 2 = x * 6[/tex]
Simplify. First, multiply, then isolate the x by dividing 6 from both sides:
[tex]7.5 * 2 = 6x\\15 = 6x\\\frac{15}{6} = \frac{6x}{6} \\x = \frac{15}{6} = 2.5[/tex]
Plug in 2.5 for x in the equation to see if the equation comes out true:
[tex]\frac{2}{6} = \frac{2.5}{7.5}\\[/tex]
Multiply 6 and 7.5 to both sides of the equation:
[tex]6 * 7.5 * \frac{2}{6} = \frac{2.5}{7.5} * 7.5 * 6\\7.5 * 2 = 2.5 * 6\\15 = 15[/tex](True)
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2.5 is your answer for x.
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