Quadrilateral sides in ratio 2:3:4:5 with perimeter 280 m: Find the exact length (in metres) of the longest side.

Introduction / Context:When the sides of a polygon are in a given ratio and the perimeter is known, multiply the sum of the ratio parts by a common scale factor to match the perimeter and then identify requested side lengths.

Given Data / Assumptions:

• Side ratio: 2 : 3 : 4 : 5.
• Perimeter = 280 m.

Concept / Approach:Let the common factor be k. Then the sides are 2k, 3k, 4k, 5k and perimeter is (2+3+4+5)k = 14k. Compute k and find the longest side 5k.

Step-by-Step Solution:

Verification / Alternative check:All sides: 40, 60, 80, 100 sum to 280 → matches the given perimeter.

Why Other Options Are Wrong:150m, 175m, 180m, 120m do not equal 5k when k = 20 from the exact perimeter constraint.

Common Pitfalls:Using average or guessing without computing k; or mis-summing the ratio parts (they total 14).

Final Answer:100m