The lengths of the sides are x, y, and z. A note indies the figure is not drawn to scale.

Question

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?

Accepted Answer

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 = 9 units and y = 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 = 6 . Therefore, if x = 9 units and y = 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.

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