Question

An isosceles triangle has two sides of equal length. The third side is 7 inches and the perimeter is 41 inches. What is the length of each of the two equal​ sides? Define a variable for the unknown quantity. Write and solve an equation to answer the question.

Answer 1

The length of each of the two equal sides in the isosceles triangle is 17 inches, found by defining a variable x for the unknown lengths, setting up the equation 2x + 7 = 41 which represents the perimeter, and solving for x.

Step-by-step explanation:

To solve the problem about the length of the two equal sides of an isosceles triangle, we will define a variable for the unknown lengths. Let x be the length of one of the two equal sides. The triangle has three sides, and we're given that the third side is 7 inches while the perimeter is 41 inches. Using the perimeter formula, which is the sum of all sides, we can set up the equation:

x + x + 7 = 41

Combine the like terms:

2x + 7 = 41

Subtract 7 from both sides to isolate the variable terms:

2x = 34

Divide both sides by 2 to find the value of x:

x = 17

Therefore, each of the two equal sides of the isosceles triangle is 17 inches long.