Question

The bulletin board is in the shape of a square. Find two rational numbers that are within 1/8 in of the actual side length.

Answer 1

See the image of the bulletin board in the shape of a square that is included in the question.

And the answer may be 3/8 and 11/8 (among an infinite amount of different rational numbers less than 188 of the actual side length), as shwon below.

Step-by-step explanation:

1) Calculate the side length of the bulletin board in the shape of a square:

The area of a square is equal to the square of length of the sides

• A = x²

Substitute A = 150 unit²

• 150 = x²

Extract square root of both sides:

• 
  `√(150) =x`

2) Find two rational numbers that are within, this is they are less than, 1/8 of the actual side length:
`√(150)`

• 
  `x<√(150)/8`

Since, 12² = 144 and 13² = 169, the square root of 150 is between 12 and 13.

Then, you can pick any two whole numbers less than 13 and multiple them by 1/8.

Remember that multiplying by 1/8 is the same that dividing by 8.

Choose 12 and 11, for instance, and two rational numbers that are less than 1/8 of the actual side length are 12/8 and 11/8.

• 12/8 can be simplified to 3/2 and 11/8 is in its simplest form.

Thus, two rational numbers that are within 1/8 of the actual side length of the bulletin board are 3/2 and 11/8.