Help with #8 please!

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

∵ =

∴ 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

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction