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Geometry and Trigonometry / Area and volume Difficulty: Easy

The triangle shown has a perimeter of $22$ units. If $x equals 9$ units and $y equals 7$ units, what is the value of $z$ , in units?

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Explanation

Choice A is correct. The perimeter of a triangle is the sum of the lengths of its three sides. The triangle shown has side lengths $x$ , $y$ , and $z$ . It's given that the triangle has a perimeter of $22$ units. Therefore, $x + y + z = 22$ . If $x equals 9$ units and $y equals 7$ units, the value of $z$ , in units, can be found by substituting $9$ for $x$ and $7$ for $y$ in the equation $x + y + z = 22$ , which yields $9 + 7 + z = 22$ , or $16 + z = 22$ . Subtracting $16$ from both sides of this equation yields $z equals 6$ . Therefore, if $x equals 9$ units and $y equals 7$ units, the value of $z$ , in units, is $6$ .

Choice B is incorrect. This is the value of $y$ , in units, not the value of $z$ , in units.

Choice C is incorrect. This is the value of $x$ , in units, not the value of $z$ , in units.

Choice D is incorrect. This is the value of $x + y$ , in units, not the value of $z$ , in units.