A rectangular field has a 4 m breadth and a 5 m diagonal length. What is its total area?
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Answer: A. 12 sq m
Explanation
The Pythagorean theorem relates rectangle length, breadth, and diagonal measurements. Squaring the diagonal five and subtracting squared breadth four gives squared length nine. The length equals three meters, which multiplied by breadth four gives twelve square meters. Right-angled triangles formed by rectangle diagonals obey the classic Pythagorean theorem. Area of a rectangle equals the product of its measured length and breadth. Integer side lengths forming right triangles are known as Pythagorean triples.
Carpenters and builders verify square corners in construction using diagonal measurement checks. Land surveyors calculate rectangular plot areas from boundary lengths and diagonal lines. Screen resolution and geometry calculations rely on diagonal Pythagorean relationships. Option twelve square meters is correct, making other choices incorrect variations. Option four root fourteen square meters miscalculates the side length and area product. Option twenty square meters multiplies length and breadth incorrectly using the diagonal.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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