A rectangular yard with side lengths in a 4:3 proportion incurs a paving expense of Rs.600 at 50 p per m2; calculate the length of the yard's diagonal.
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Answer: D. 50 m
Explanation
The total area is calculated by dividing the paving expense by the cost per square meter. Using side lengths four x and three x yields twelve x squared equal to twelve hundred. Solving for x gives ten, making the side dimensions forty and thirty meters respectively. Pythagorean theorem states that the diagonal of a rectangle equals the square root of length squared plus width squared. Area of a rectangular yard equals its length multiplied by its corresponding width dimension. A right triangle with sides of thirty and forty meters features a hypotenuse of fifty meters.
Property surveyors calculate diagonals to verify that rectangular land plots feature true right angles. Construction workers use diagonal measurements to ensure foundations are perfectly square before pouring concrete. Fencing estimates require knowing both perimeter and diagonal dimensions for complex irregular yards. Option A is too small and represents half of the correct diagonal calculation. Option B results from an incorrect proportional scaling of the rectangular side dimensions. Option C is an incorrect intermediate value that does not satisfy the Pythagorean theorem.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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