CAN YOU SOLVE IT?(By vikash rahii)
In the square below, a line is drawn from the bottom left corner with length 12 to the interior of the square. From the end of that line, a perpendicular is drawn going up and left with length 3. From the end of that line, another perpendicular is drawn going up and right with length 9. This line segment ends at the upper right corner of the square.
What is the value of x, the square’s side length?
The problem took me a little while to solve. I considered drawing the hypotenuses of various triangles, and I also tried using coordinate geometry. But I could not get these approaches to work.
Then I thought, what would happen if I rotated the diagram so the line segments with 12 and 9 were horizontal?
Then it struck me: we can find the distance between the endpoints by forming a right triangle where the bottom leg is 12 + 9 = 21 and the other leg is 3.
The hypotenuse is then:
212 + 32 = 441 + 9 = 450 = c2
c = √450 = 15√2
This distance equals the diagonal of the square.
The diagonal of a square is the hypotenuse of an isosceles right triangle, so its length is x√2.
Thus we have x√2 = 15√2 so x = 15.
In the square below, a line is drawn from the bottom left corner with length 12 to the interior of the square. From the end of that line, a perpendicular is drawn going up and left with length 3. From the end of that line, another perpendicular is drawn going up and right with length 9. This line segment ends at the upper right corner of the square.
What is the value of x, the square’s side length?
The problem took me a little while to solve. I considered drawing the hypotenuses of various triangles, and I also tried using coordinate geometry. But I could not get these approaches to work.
Then I thought, what would happen if I rotated the diagram so the line segments with 12 and 9 were horizontal?
Then it struck me: we can find the distance between the endpoints by forming a right triangle where the bottom leg is 12 + 9 = 21 and the other leg is 3.
The hypotenuse is then:
212 + 32 = 441 + 9 = 450 = c2
c = √450 = 15√2
This distance equals the diagonal of the square.
The diagonal of a square is the hypotenuse of an isosceles right triangle, so its length is x√2.
Thus we have x√2 = 15√2 so x = 15.
The square's side length puzzle.
Reviewed by biharishayar
on
November 13, 2017
Rating:
Reviewed by biharishayar
on
November 13, 2017
Rating:
Nice.....we. .
ReplyDeleteGoods teaching Sir.....
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