Question

A hexagon has 3 sides of the same length, two sides that are each 2/3 that length, and a sixth side that is 14.5 cm. The perimeter is 86 cm. Write and solve an equation to find the length of one of the SMALLEST sides.

a) 8 cm
b) 12 cm
c) 6 cm
d) 10 cm

Answer 1

To find the length of one of the smallest sides of the hexagon, we can set up an equation using the perimeter information and solve for x. The length of one of the smallest sides is approximately 10 cm.

Step-by-step explanation:

To find the length of one of the smallest sides of the hexagon, we need to first find the length of the other sides. Let's denote the length of the equal sides as x. The two sides that are 2/3 of that length would be (2/3)x. The sixth side is given as 14.5 cm. We can set up an equation using the perimeter information:

x + x + x + (2/3)x + (2/3)x + 14.5 = 86

Combining like terms, we get:

3x + (4/3)x + 14.5 = 86

7x + 14.5 = 86

Subtracting 14.5 from both sides, we get:

7x = 71.5

Dividing both sides by 7, we find:

x = 10.21 cm

Therefore, the length of one of the smallest sides of the hexagon is approximately 10 cm (option d).