Question

Triangle GEO is an isosceles triangle with vertex angle O, GE = 11x + 6, EO = 12x-4, and GO = 10x + 12. Determine the length of the BASE of the triangle.

Answer 1

The length of the base of Triangle GEO, an isosceles triangle with vertex angle O, is 112 units. To find it, we equated the expressions for GE and EO, solved for x, and then substituted x into the expression for GO which is the base of the triangle.

Step-by-step explanation:

To determine the length of the base of Triangle GEO, which is an isosceles triangle with vertex angle O, we must remember that in an isosceles triangle, the two sides that are equal are the legs, and the base is the third side. In this case, since GE and EO are given as functions of x, and they are not equal, they cannot be the legs, so GO must be the base.

We are given:

GE = 11x + 6,

EO = 12x - 4,

GO (the base) = 10x + 12.

In an isosceles triangle, the legs are equal, so we can set GE equal to EO:

• 11x + 6 = 12x - 4

Solving for x, we find:

• x = 10

Now we can substitute x into the expression for the base GO:

• GO = 10(10) + 12
• GO = 100 + 12
• GO = 112

Therefore, the length of the base of Triangle GEO is 112 units.