Question

The sides of a triangle are in a 2 : 3 : 4 ratio. What is the length of the longest side if the perimeter of the triangle is 63 in.?

1) 21 in.
2) 14 in.
3) 7 in.
4) 28 in.

Answer 1

The length of the longest side of the triangle is 28 inches.

Step-by-step explanation:

To find the length of the longest side of the triangle, we need to determine the actual lengths of the sides using the given ratio and the perimeter. Let the sides be 2x, 3x, and 4x, where x is a common factor. The perimeter of the triangle is the sum of the lengths of its sides, so we have:

2x + 3x + 4x = 63

9x = 63

x = 7

Therefore, the lengths of the sides are 2x = 2(7) = 14, 3x = 3(7) = 21, and 4x = 4(7) = 28. The longest side is 28 inches. So, the correct answer is 4) 28 in.