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The ends of a diagonal of a square have the coordinates (a, 1) and (-1, a), find a if the area of the square is 50 square units.
- a)±7
- b)±5
- c)±6
- d)±4
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The ends of a diagonal of a square have the coordinates (a, 1) and (-1...
Let side of the square be x.
x2 + x2 = (-1 -a)2 + (a - 1)2
⇒ 2x2 = 1 + a2 + 2a + a2 + 1 - 2a
⇒ x2 = a2 + 1
⇒ 50 = a2 + 1 ⇒ a2 = 49
⇒ a = ±7
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The ends of a diagonal of a square have the coordinates (a, 1) and (-1...
To find the length of the diagonal of the square, we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the length of the diagonal of the square:
d = sqrt((-1 - a)^2 + (a - 1)^2)
d = sqrt((1 + 2a + a^2) + (a^2 - 2a + 1))
d = sqrt(2a^2 + 2)
d = sqrt(2(a^2 + 1))
Since the diagonal of a square is the hypotenuse of a right triangle formed by two sides of the square, we can use the Pythagorean theorem to find the length of each side of the square:
s^2 + s^2 = d^2
2s^2 = 2(a^2 + 1)
s^2 = a^2 + 1
s = sqrt(a^2 + 1)
The area of the square is given by the formula A = s^2, so we can substitute the expression for s:
A = (sqrt(a^2 + 1))^2
A = a^2 + 1
We are given that the area of the square is 50, so we can set up the equation:
50 = a^2 + 1
Subtracting 1 from both sides:
49 = a^2
Taking the square root of both sides:
a = ±7
Therefore, the value of a can be either 7 or -7.
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the length of the diagonal of the square:
d = sqrt((-1 - a)^2 + (a - 1)^2)
d = sqrt((1 + 2a + a^2) + (a^2 - 2a + 1))
d = sqrt(2a^2 + 2)
d = sqrt(2(a^2 + 1))
Since the diagonal of a square is the hypotenuse of a right triangle formed by two sides of the square, we can use the Pythagorean theorem to find the length of each side of the square:
s^2 + s^2 = d^2
2s^2 = 2(a^2 + 1)
s^2 = a^2 + 1
s = sqrt(a^2 + 1)
The area of the square is given by the formula A = s^2, so we can substitute the expression for s:
A = (sqrt(a^2 + 1))^2
A = a^2 + 1
We are given that the area of the square is 50, so we can set up the equation:
50 = a^2 + 1
Subtracting 1 from both sides:
49 = a^2
Taking the square root of both sides:
a = ±7
Therefore, the value of a can be either 7 or -7.
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The ends of a diagonal of a square have the coordinates (a, 1) and (-1, a), find a if the area of the square is 50 square units.a)±7b)±5c)±6d)±4Correct answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The ends of a diagonal of a square have the coordinates (a, 1) and (-1, a), find a if the area of the square is 50 square units.a)±7b)±5c)±6d)±4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ends of a diagonal of a square have the coordinates (a, 1) and (-1, a), find a if the area of the square is 50 square units.a)±7b)±5c)±6d)±4Correct answer is option 'A'. Can you explain this answer?.
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