The four sides of a quadrilateral are in the ratio 2:3:4:5 and its total perimeter is 280 m. Find the length of the longest side of the quadrilateral in metres.

Introduction / Context:
This is a simple ratio and perimeter question involving a quadrilateral. The sides are described as being in a fixed ratio. We use this ratio to represent each side as a multiple of a common variable. Adding these sides gives the perimeter in terms of that variable, which can then be equated to the actual perimeter to find the value of the variable. After that, each side length can be found, and we select the longest one.

Given Data / Assumptions:

• Side ratio: 2 : 3 : 4 : 5.
• Perimeter of quadrilateral = 280 m.
• Let common multiplying factor be k.
• Each side = 2k, 3k, 4k, and 5k respectively.

Concept / Approach:
When lengths are in a ratio, each length can be written as that ratio number multiplied by a common factor. The sum of the sides is the perimeter. So (2k + 3k + 4k + 5k) must equal 280. Solving this equation gives k. The largest side is the one associated with the largest ratio number, which is 5k. We compute that and express the length in metres.

Step-by-Step Solution:
Let the sides be 2k, 3k, 4k, and 5k.Perimeter = 2k + 3k + 4k + 5k.Sum of coefficients = 2 + 3 + 4 + 5 = 14.So perimeter = 14k.Given perimeter = 280 m, so 14k = 280.k = 280 / 14 = 20.Longest side corresponds to 5k = 5 * 20 = 100 m.

Verification / Alternative check:
To confirm, calculate all side lengths: 2k = 40 m, 3k = 60 m, 4k = 80 m, and 5k = 100 m. Adding them gives 40 + 60 + 80 + 100 = 280 m, which matches the given perimeter. The sides clearly preserve the ratio 2 : 3 : 4 : 5, confirming that k = 20 is correct and the longest side is indeed 100 m.

Why Other Options Are Wrong:
150 m, 175 m, and 180 m do not fit the ratio pattern when combined with three other sides that should still sum to 280 m. For instance, if the longest side were 175 m, the remaining sides would need to sum to 105 m and still be in the ratio 2:3:4, which is not possible. 120 m similarly fails when checked against the ratio and total perimeter. Only 100 m fits consistently with the given ratio and perimeter.

Common Pitfalls:
Some learners divide 280 by the largest ratio number 5 instead of the sum of all ratio parts. Others mistakenly assume each side is directly 2 m, 3 m, 4 m, and 5 m, ignoring the perimeter condition. Remember that you must use the sum of ratio numbers to find the correct scaling factor for all sides simultaneously.

Final Answer:
100 m