A rectangle's length and breadth are in a 5:4 ratio. Find its perimeter if its area is 180 cm²
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Answer: A. 54 cm
Explanation
Algebraic variables represent the length and breadth using the given five to four ratio. Multiplying length and breadth gives an area expression that equals one hundred eighty square centimeters. Solving for the variable yields dimensions of fifteen and twelve, resulting in a perimeter of fifty four. Ratio problems use a common multiplier variable to express proportional side lengths algebraically. Rectangle area is the product of length and breadth, while perimeter is twice their sum. Solving quadratic area equations allows finding exact linear dimensions for geometric shapes.
Proportional sizing is widely used in photography, screen design, and architectural drafting. Calculating perimeters from areas is essential when estimating boundary fencing for scaled plots. Algebraic word problems bridge abstract mathematical equations with tangible geometric figures. Option b suggests twenty seven centimeters which represents only half of the calculated perimeter. Option c provides twelve centimeters which matches a single side dimension rather than the perimeter. Option d gives fifteen centimeters which corresponds to the rectangle length alone.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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