Answer:
8. The length of the longest side is 40 ⇒ H
Step-by-step explanation:
8. In the given figure
∵ The triangle has two equal sides 2x + 12 and 5x - 9
→ Equate their expressions to find the value of x
∴ 5x - 9 = 2x + 12
→ Add 9 to both sides
∵ 5x - 9 + 9 = 2x + 12 + 9
∴ 5x = 2x + 21
→ Subtract 2x from both sides
∵ 5x - 2x = 2x - 2x + 21
∴ 3x = 21
→ Divide both sides by 3 to find x
∵ [tex]\frac{3x}{3}[/tex] = [tex]\frac{21}{3}[/tex]
∴ x = 7
∵ The longest side is 6x - 2
→ Substitute the value of x in its expression to find its length
∴ The longest side = 6(7) - 2 = 42 - 2
∴ The longest side = 40
∴ The length of the longest side is 40
