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In the figure below, FGHJ is a square and Q, R, S, and T are the midpoints of its sides. If  inches, what is the area of QRST, in inches?
  • a)
    100
  • b)
    50
  • c)
    25
  • d)
    20
  • e)
    5√2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In the figure below, FGHJ is a square and Q, R, S, and T are the midpo...
To find the area of QRST, first determine the length of its sides. To do so, use the fact that right triangles exist in every corner of FGHJ with legs that are equal to half the length of a side of FGHJ, and with hypotenuse equal to the length of a side of QRST. Since the length of a side of FGHJ is 10, the legs of the triangles have length 5. Using the Pythagorean Theorem, the length of the hypotenuse, h, is expressed by h2 = 52 + 52 = 25 + 25 = 50; h = √50. Since the length of the hypotenuse is equal to the length of a side of QRST, the area of QRST is (√50)2, or 50.
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In the figure below, FGHJ is a square and Q, R, S, and T are the midpoints of its sides. If inches, what is the area of QRST, in inches?a)100b)50c)25d)20e)5√2Correct answer is option 'B'. Can you explain this answer?
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