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The lengths of the sides of a triangle are 3 consecutive even integers. If the perimeter of the triangle is 48 inches, what is the length, in inches, of the longest side?
- a)12
- b)14
- c)16
- d)18
- e)24
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The lengths of the sides of a triangle are 3 consecutive even integers...
To solve this problem, first remember that perimeter is equal to the distance around an object. Therefore, the perimeter of a triangle is simply the sum of the lengths of its sides. You are given that the lengths of the sides of the triangle are 3 consecutive even integers. Set the first length (the shortest side) equal to x, the second length equal to x + 2, and the third length (the longest side) equal to x + 4. Now, create an equation and solve for x, as follows:
x + (x + 2) + (x + 4) = 48
3x + 6 = 48
x = 14
You now know that the length of the shortest side is 14, so the length of the longest side must be 14 + 4 = 18.
x + (x + 2) + (x + 4) = 48
3x + 6 = 48
x = 14
You now know that the length of the shortest side is 14, so the length of the longest side must be 14 + 4 = 18.
Most Upvoted Answer
The lengths of the sides of a triangle are 3 consecutive even integers...
Given:
- The lengths of the sides of a triangle are 3 consecutive even integers.
- The perimeter of the triangle is 48 inches.
To find:
- The length, in inches, of the longest side of the triangle.
Solution:
Let's assume the three consecutive even integers as x, x+2, and x+4.
Perimeter:
The perimeter of a triangle is the sum of the lengths of its sides.
So, the perimeter of this triangle can be calculated as:
x + (x+2) + (x+4) = 48
Simplifying the equation:
3x + 6 = 48
3x = 42
x = 14
Lengths of the sides:
The lengths of the sides of the triangle are 14, 16, and 18 inches (as x=14).
The longest side:
The longest side of the triangle is 18 inches.
Therefore, the correct answer is option 'D' (18).
- The lengths of the sides of a triangle are 3 consecutive even integers.
- The perimeter of the triangle is 48 inches.
To find:
- The length, in inches, of the longest side of the triangle.
Solution:
Let's assume the three consecutive even integers as x, x+2, and x+4.
Perimeter:
The perimeter of a triangle is the sum of the lengths of its sides.
So, the perimeter of this triangle can be calculated as:
x + (x+2) + (x+4) = 48
Simplifying the equation:
3x + 6 = 48
3x = 42
x = 14
Lengths of the sides:
The lengths of the sides of the triangle are 14, 16, and 18 inches (as x=14).
The longest side:
The longest side of the triangle is 18 inches.
Therefore, the correct answer is option 'D' (18).
Community Answer
The lengths of the sides of a triangle are 3 consecutive even integers...
To solve this problem, first remember that perimeter is equal to the distance around an object. Therefore, the perimeter of a triangle is simply the sum of the lengths of its sides. You are given that the lengths of the sides of the triangle are 3 consecutive even integers. Set the first length (the shortest side) equal to x, the second length equal to x + 2, and the third length (the longest side) equal to x + 4. Now, create an equation and solve for x, as follows:
x + (x + 2) + (x + 4) = 48
3x + 6 = 48
x = 14
You now know that the length of the shortest side is 14, so the length of the longest side must be 14 + 4 = 18.
x + (x + 2) + (x + 4) = 48
3x + 6 = 48
x = 14
You now know that the length of the shortest side is 14, so the length of the longest side must be 14 + 4 = 18.
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The lengths of the sides of a triangle are 3 consecutive even integers. If the perimeter of the triangle is 48 inches, what is the length, in inches, of the longest side?a)12b)14c)16d)18e)24Correct answer is option 'D'. Can you explain this answer?
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