forming and solving equations question.....?

Question

the sides of a regular octagon are x cm long. Each side of a regular pentagon is 6cm longer than each side of the octagon. The perimeter of the octagon is 3cm longer than the perimeter of the pentagon.

a) write down an equation that x satisfies.

b)solve the equation and hence find the length of a side of the pentagon.


thanks!

Answer 1

a.)
Step 1: Write an equation for each sentence.
p = 6 + x (where p is side of a pentagon)
8x = 5p + 3

Step 2: Substitute to create 1 equation with x.
8x = 5(6 + x) + 3 (solution for a)

Step 3: Simplify and solve.
8x = 30 + 5x + 3
3x = 33
x = 11 cm
p = 6 + x = 6 + 11 = 17 cm (solution for b).