Question

perpendicular bisector of an isosceles triangle
find the value of x. perpend,
7x + 24
13x - 48

1. select all that apply:

perpendicular
forms four right
angles with a side if it
goes through the
side between its
endpoint.
forms two 90° angles
with a side if it only
touches the side
between its
endpoints.
forms a right angle
with a side if it only
touches the side at
its endpoint.

Explanation:

Step1: Set the two expressions equal

Since the perpendicular bisector in an isosceles triangle implies the two sides are equal, we set \(7x + 24 = 13x - 48\).

Step2: Solve for x

Subtract \(7x\) from both sides: \(24 = 6x - 48\).
Add 48 to both sides: \(72 = 6x\).
Divide both sides by 6: \(x = \frac{72}{6} = 12\).

Answer:

\(x = 12\)