Two sides of a triangle have equal length. The third side is seven inches shorter. How long are the three sides if the perimeter is 23 inches?
Let x equal the two sides of equal length.
2x + (x - 7) = 23
3x - 7 = 23
3x = 30
x = 10
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To solve this problem, let's break it down step by step:
Step 1: Understand the problem
We have a triangle where two sides have equal lengths and the third side is seven inches shorter than the other two. The perimeter of the triangle is given as 23 inches. We need to determine the lengths of the three sides.
Step 2: Define the variables
Let's define the length of one side of the triangle as "x" inches. Since two sides have equal lengths, the other side will also be "x" inches. The length of the third side will be "x - 7" inches.
Step 3: Write the equation
The perimeter of a triangle is the sum of the lengths of its three sides. In this case, the equation is: x + x + (x - 7) = 23.
Step 4: Solve the equation
Combine like terms: 2x + x - 7 = 23.
Combine x terms: 3x - 7 = 23.
Add 7 to both sides: 3x = 30.
Divide both sides by 3: x = 10.
Step 5: Find the lengths of the sides
The length of the first two sides is x, which is 10 inches. The length of the third side is x - 7, which is 10 - 7 = 3 inches.
So, the lengths of the three sides of the triangle are 10 inches, 10 inches, and 3 inches.