Question

The perimeter of the triangle is the same length as the perimeter of the square 3a−2, 3a−1, 2a+7

Find an expression for the length of one side of the square in terms of a. Give your answer in its simplest form.

Option A: a−2
Option B: a−3
Option C: a+5
Option D: a+4

Answer 1

The length of one side of the square in terms of a is 2a + 1. This is obtained by adding the expressions for the triangle's sides to get 8a + 4, which is equivalent to the perimeter of the square (4s), and then dividing by 4 to get s = 2a + 1.

Step-by-step explanation:

The question provides the lengths of the sides of a triangle, which have the same total perimeter as a square. To find the expression for the length of one side of that square in terms of the variable a, we must first calculate the perimeter of the triangle by adding the lengths of its sides: 3a - 2, 3a - 1, and 2a + 7. This sum will be equal to the total perimeter of the square, which can be written as 4s, where s represents the length of one side of the square.

The sum of the lengths of the sides of the triangle is:

• (3a - 2) + (3a - 1) + (2a + 7) = 3a + 3a + 2a - 2 - 1 + 7 = 8a + 4

Since the perimeter of the square is four times the length of one side (4s), we have:

• 8a + 4 = 4s

To find the length of one side of the square, we divide both sides by 4:

• (8a + 4) / 4 = s
• 2a + 1 = s

Therefore, the length of one side of the square, in terms of a, is 2a + 1. This is not one of the options provided in the question, implying there may be a mistake in the options given or a typo in the expressions presented for the triangle's sides.