Question

Find the length of x

Answer 1

x = 2.5

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
`(base)/(hypotenuse)`

Set the equation:

`(2)/(6) = (x)/(7.5)`

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:

`7.5 * 6 * ((2)/(6)) = ((x)/(7.5)) * 6 * 7.5\\7.5 * 2 = x * 6`

Simplify. First, multiply, then isolate the x by dividing 6 from both sides:

`7.5 * 2 = 6x\\15 = 6x\\(15)/(6) = (6x)/(6) \\x = (15)/(6) = 2.5`

Plug in 2.5 for x in the equation to see if the equation comes out true:

`(2)/(6) = (2.5)/(7.5)\\`

Multiply 6 and 7.5 to both sides of the equation:

`6 * 7.5 * (2)/(6) = (2.5)/(7.5) * 7.5 * 6\\7.5 * 2 = 2.5 * 6\\15 = 15`(True)

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2.5 is your answer for x.

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