Question

Write an equation and define the variable for the following problem. Do not solve.

The perimeter of a triangle is 39 inches. The second side is 9 times as long as the first side. The third side is 1 inch shorter than the second side.

My equation: ________
Let ________ = ________

a) P = 39; x = first side length
b) P = 39; x = second side length
c) P = 39; x = third side length
d) P = 39; x = total side length

Answer 1

An equation representing the perimeter of the triangle with given conditions is P = x + 9x + (9x - 1), where x is the first side length, and the correct answer is a) P = 39; x = first side length.

Step-by-step explanation:

To write an equation for the given triangle problem, we need to define our variable and understand the relationships between the sides of the triangle. Let's choose the first side as our variable for simplicity. So, let x be the length of the first side in inches. According to the problem, the second side is 9 times as long as the first side, which means the second side's length is 9x inches. The third side is 1 inch shorter than the second side, so the third side's length is 9x - 1 inches. The perimeter of the triangle, which is the sum of the lengths of its three sides, is given as 39 inches.

Therefore, the equation to represent the perimeter of the triangle is:

P = x + 9x + (9x - 1)

When we define the variable:

Let x = first side length

The correct answer from the given options is a) P = 39; x = first side length.