The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?
A. $6.2+b=14.5$
B. $9.3+b=14.5$
C. $12.4+b=14.5$
D. $18.6+b=14.5
Answer (2)
Define the shortest side as a , the middle side as b , and the longest side as c , where c = 6.2 cm.
Use the relationship c = 2 a to find the shortest side: a = 2 6.2 = 3.1 $
cm.
Substitute the values of a and c into the perimeter equation: a + b + c = 14.5 becomes 3.1 + b + 6.2 = 14.5 .
Simplify the equation to find the equation that can be used to solve for b : 9.3 + b = 14.5 .
Explanation
Analyze the problem Let's analyze the problem. We are given the perimeter of a scalene triangle, which is 14.5 cm. We also know that the longest side is twice the shortest side, and the longest side measures 6.2 cm. Our goal is to find the equation that can be used to find the side lengths of the triangle.
Define the sides Let a be the shortest side, b be the middle side, and c be the longest side. We are given that c = 6.2 cm and c = 2 a .
Calculate the shortest side We can find the length of the shortest side a using the information c = 2 a . Since c = 6.2 cm, we have 6.2 = 2 a . Dividing both sides by 2, we get a = 2 6.2 = 3.1 $ cm.
Write the perimeter equation The perimeter of the triangle is the sum of the lengths of its sides: a + b + c = 14.5 cm. We know that a = 3.1 cm and c = 6.2 cm. Substituting these values into the perimeter equation, we get 3.1 + b + 6.2 = 14.5 .
Simplify the equation Simplifying the equation, we combine the known values: 3.1 + 6.2 = 9.3 . So the equation becomes 9.3 + b = 14.5 .
State the final equation Therefore, the equation that can be used to find the side lengths is 9.3 + b = 14.5 .
Examples
Understanding triangle perimeters is useful in many real-world scenarios. For example, if you're building a triangular garden bed and need to determine how much fencing to buy, knowing the perimeter is essential. If you know the length of one side and a relationship between the sides, you can calculate the remaining side lengths to ensure you purchase the correct amount of fencing. In this case, if the longest side of your garden bed is 6.2 meters and is twice the shortest side, you can determine the length of the shortest side and then use the perimeter to find the length of the remaining side. The equation 9.3 + b = 14.5 helps you find the length of the remaining side.
The equation that can be used to find the side lengths of the scalene triangle is 9.3 + b = 14.5 . This comes from the relationships between the sides and the total perimeter of the triangle. Therefore, the correct choice is option B.
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