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ABCD is a square of 20 m. What is the area of the least-sized square that can be inscribed in it with its vertices on the sides of ABCD?
- a)120 m²
- b)100 m²
- c)200 m²
- d)250 m²
- e)None
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
ABCD is a square of 20 m. What is the area of the least-sized square t...
It touches on midpoints on the sides of the square ABCD:
Side= √(10^2 +10^2) = √200
So, Area = 200 m^2
Most Upvoted Answer
ABCD is a square of 20 m. What is the area of the least-sized square t...
The area of the inscribed square is equal to the area of the square ABCD multiplied by the ratio of the side length of the inscribed square to the side length of ABCD. Let x be the length of the side of the inscribed square. Then:
x/20 = 1/√2
Solving for x, we get:
x = 20/√2
The area of the inscribed square is then:
x^2 = (20/√2)^2 = 200
Therefore, the area of the least-sized square that can be inscribed in square ABCD with its vertices on the sides of ABCD is 200 square meters. Answer: \boxed{200}.
x/20 = 1/√2
Solving for x, we get:
x = 20/√2
The area of the inscribed square is then:
x^2 = (20/√2)^2 = 200
Therefore, the area of the least-sized square that can be inscribed in square ABCD with its vertices on the sides of ABCD is 200 square meters. Answer: \boxed{200}.
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ABCD is a square of 20 m. What is the area of the least-sized square that can be inscribed in it with its vertices on the sides of ABCD?a)120 m²b)100 m²c)200 m²d)250 m²e)NoneCorrect answer is option 'C'. Can you explain this answer?
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