Question

In △jlp , m∠jmp=(3x−6)° , jk=3y−2 , and lk=5y−8 . if jm⎯⎯⎯⎯⎯ is an altitude of △jlp , find the value of x.

Answer 1

To find the value of x, we set the angle measure (3x−6)° equal to 90°, because JM is an altitude, making △jmp a right triangle. Solving the equation gives us x = 32.

Step-by-step explanation:

The problem describes a triangle △jlp with an altitude, and provides expressions for an angle measure and side lengths involving variables x and y. We are tasked with finding the value of x given that JM is an altitude and therefore, △jmp is a right triangle.

The measure of ∠jmp is given as (3x−6)°. Since △jmp is a right triangle, and JM is an altitude, ∠jmp must be 90°. We can set up the equation (3x−6)° = 90° and solve for x:

1. 3x − 6 = 90
2. 3x = 96
3. x = 32

So the value of x is 32.