A wall pennant is in the shape of an isosceles triangle. Each of the two equal sides measures 18 in more than the third side, and the perimeter of the triangle is 54in. What are the lengths of the sides of the pennant?
x + x + 18 + x + 18 = 54
3x = 18
x = 6
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To find the lengths of the sides of the pennant, we can start by setting up equations based on the given information.
Let's denote the length of the third side as "x" inches. According to the problem, each of the two equal sides measures 18 inches more than the third side. Therefore, the lengths of the two equal sides can be represented as "x + 18" inches.
The perimeter of the triangle is the sum of all three sides. In this case, the perimeter is given as 54 inches. So, we can write the equation:
x + (x + 18) + (x + 18) = 54
We can simplify this equation by combining like terms:
3x + 36 = 54
Now, subtract 36 from both sides of the equation to isolate the variable:
3x = 54 - 36
3x = 18
Next, divide both sides of the equation by 3 to solve for x:
x = 18 / 3
x = 6
So, the length of the third side is 6 inches.
To find the lengths of the equal sides, substitute the value of x back into the equations:
Length of each equal side = x + 18
Length of each equal side = 6 + 18
Length of each equal side = 24
Therefore, the lengths of the sides of the pennant are 6 inches, 24 inches, and 24 inches.