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If the diagonal of a square becomes half, the area of that square reduces by how much percentage?
- a)40%
- b)50%
- c)25%
- d)75%
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If the diagonal of a square becomes half, the area of that square redu...
Let diagonal of the square be d units.
Area of square = (1/2) d2 If diagonal of the square is reduced by half, then the new area of the square = (1/2) × (d/2)2 = (1/8) d2 So, reduction in the area of the square = (1/2)d2 – (1/8)d2 = (3/8) d2
The percentage by which the area of that square gets reduced = [{(3/8)d2} / {(1/2)d2}] × 100 = 75% Hence, option (d) is correct.
Area of square = (1/2) d2 If diagonal of the square is reduced by half, then the new area of the square = (1/2) × (d/2)2 = (1/8) d2 So, reduction in the area of the square = (1/2)d2 – (1/8)d2 = (3/8) d2
The percentage by which the area of that square gets reduced = [{(3/8)d2} / {(1/2)d2}] × 100 = 75% Hence, option (d) is correct.
Most Upvoted Answer
If the diagonal of a square becomes half, the area of that square redu...
Explanation:
The area of a square is given by the formula A = side x side. When the diagonal of a square becomes half, it means that the side of the square also becomes half.
Calculating the initial area of the square:
Let's assume the side of the original square is 'S'.
Therefore, the area of the original square = S x S = S^2.
Calculating the new area of the square after the diagonal becomes half:
Since the diagonal becomes half, the side of the square also becomes half.
Let 'S/2' be the side of the new square.
Therefore, the area of the new square = (S/2) x (S/2) = S^2 / 4.
Calculating the percentage decrease in the area:
Percentage decrease = ((Initial area - New area) / Initial area) x 100%
Percentage decrease = ((S^2 - S^2 / 4) / S^2) x 100%
Percentage decrease = (3/4) x 100%
Percentage decrease = 75%
Therefore, the area of the square reduces by 75% when the diagonal becomes half. Hence, the correct answer is option 'D' - 75%.
The area of a square is given by the formula A = side x side. When the diagonal of a square becomes half, it means that the side of the square also becomes half.
Calculating the initial area of the square:
Let's assume the side of the original square is 'S'.
Therefore, the area of the original square = S x S = S^2.
Calculating the new area of the square after the diagonal becomes half:
Since the diagonal becomes half, the side of the square also becomes half.
Let 'S/2' be the side of the new square.
Therefore, the area of the new square = (S/2) x (S/2) = S^2 / 4.
Calculating the percentage decrease in the area:
Percentage decrease = ((Initial area - New area) / Initial area) x 100%
Percentage decrease = ((S^2 - S^2 / 4) / S^2) x 100%
Percentage decrease = (3/4) x 100%
Percentage decrease = 75%
Therefore, the area of the square reduces by 75% when the diagonal becomes half. Hence, the correct answer is option 'D' - 75%.
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