Finding the length of each side.

Question

Each of the three longest sides of a hexagon is 3 cm less than 4 times the length of each of the three shortest sides. The perimeter is 111 cm. What is the length of each side.

Answer 1

Hello Sabrina,

Perimeter = 111 cm

Let the shortest side be 'x'

longer side, y = 4x - 3

According to question,

Perimeter of hexagon = sum of all the sides

111 = x + x + x + y + y + y

111 = 3x + 3y

111 = 3x + 3(4x-3) (substituting the value of y = 4x - 3)

111 = 3x + 12x - 9

111 = 15x - 9

111 + 9 = 15x - 9 + 9 (adding 9 on both sides)

120 = 15x

x = 120 / 15

x = 8

Therefore, shortest side, x = 8

and longest side, y = 4x - 3

y = 4(8) - 3

y = 32 - 3

y = 29

Hence, x = 8 cm and y = 29 cm

Lets verify:

111 = 3x + 3y

111 = 3(8) + 3(29)

111 = 24 + 87

111 = 111

LHS = RHS

Hence Proved!!

Happy to help :)