Question

this triangle is isosceles.
find the value of z.

(11z + 2)
(4z + 16)

(z = ?)

Explanation:

Identify the geometric properties

The diagram shows an isosceles triangle with an altitude drawn from the top vertex to the base. The tick marks on the base segments indicate that the altitude bisects the base into two equal segments. Therefore, the two segments at the bottom are equal in length.

Set up the equation

Using the given algebraic expressions for the two equal segments:

$$11z + 2 = 4z + 16$$

Solve for z

Subtract \(4z\) from both sides:

$$7z + 2 = 16$$

Subtract 2 from both sides:

$$7z = 14$$

Divide by 7:

$$z = 2$$

Answer:

This triangle is isosceles. Find the value of z.

\(z =\) <blank>2</blank>