Question

1. find the value of x and classify the triangle by its sides. (g6d)

6.______
3x + 20
6x - 7
x = 4, isosceles
x = 9, equilateral
x = 9, isosceles
x = 4, equilateral

Explanation:

Step1: Set up the equation

Since the triangle has two equal sides (given by the expressions \(3x + 20\) and \(6x-7\)), we set \(3x + 20=6x - 7\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(20 = 3x-7\).
Add \(7\) to both sides: \(27=3x\).
Divide both sides by \(3\): \(x = 9\).

Step3: Check the side lengths

Substitute \(x = 9\) into \(3x + 20\): \(3\times9+20=27 + 20=47\).
Substitute \(x = 9\) into \(6x-7\): \(6\times9-7=54 - 7=47\).
Since two sides are equal (\(47 = 47\)), the triangle is isosceles.

Answer:

\(x = 9\), isosceles