Question

1. what is the value of ( x ) and length of each side if ( \triangle abc ) is equilateral?

( x = ) 2
side length

Explanation:

Step1: Use equilateral triangle property (all sides equal). Let's take two sides, say \( 7.5x \) and \( 6x + 3 \).

Set \( 7.5x = 6x + 3 \)
Subtract \( 6x \) from both sides: \( 1.5x = 3 \)
Divide by \( 1.5 \): \( x = \frac{3}{1.5} = 2 \) (matches the given \( x = 2 \))

Step2: Calculate side length using \( x = 2 \) in any side, e.g., \( 7.5x \).

Substitute \( x = 2 \): \( 7.5 \times 2 = 15 \)
Verify with other sides: \( 6x + 3 = 6(2) + 3 = 15 \), \( 10x - 5 = 10(2) - 5 = 15 \). All equal.

Answer:

\( x = 2 \), Side length = 15