SOLUTION: Paul put some rectangular paintings on the wall. For each picture he
put one nail into the wall 2.5 m above the floor and attached a 2 m
long string at the two upper corners. Whi
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-> SOLUTION: Paul put some rectangular paintings on the wall. For each picture he
put one nail into the wall 2.5 m above the floor and attached a 2 m
long string at the two upper corners. Whi
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Question 1070239: Paul put some rectangular paintings on the wall. For each picture he
put one nail into the wall 2.5 m above the floor and attached a 2 m
long string at the two upper corners. Which of the following pictures is
closest to the floor (format: width in cm × height in cm)?
A) 60×40 B) 120×50 C) 120×90 D) 160×60 E) 160×100
nail is 250 cm above the floor.
string is 200 cm long.
to be balanced, 100 cm of the string will be on the left and 100 cm of the string will be on the right.
these 100 cm lengths will form the hypotenuse of a right triangle that has its horizontal leg equal to 1/2 the width of the picture.
the other leg of the right triangle formed will be the vertical leg which forms the distance between the nail and the top of the picture.
pythagorus formula is:
c^2 = a^2 + b^2
c is the hypotenuse.
a is the vertical leg which is the distance between the nail in the wall and the top of the picture.
b is the horizontal leg which is equal to 1/2 the width of the picture.
solve for a to get:
a = sqrt(c^2 - b^2)
since c = 100, the formula becomes a = sqrt(100^2 - b^2)
b will be either 30 or 60 or 80.
30 is half of the width of the picture whose width is 60.
60 is half of the width of the picture whose width is 120.
80 is half of the width of the picture whose width is 160.
to solve for a, you get:
when b = 30, a = sqrt(100^2 - 30^2) = 95.4
when b = 60, a = sqrt(100^2 - 60^2) = 80
when b = 80, a = sqrt(100^2 - 80^2) = 60
these are all measurements in cm.
that gets you the distance from the top of each picture to the nail.
now you have to add the length of each picture to see which picture is closest to the floor.
the picture with width of 60 has a longest height of 40, so the distance between the bottom of that picture and the nail is equal to 95.4 + 40 = 135.4 cm.
the picture with width of 120 has a longest height of 90, so the distance between the bottom of that picture and the nail is equal to 80 + 90 = 170 cm.
the picture with width of 160 has a longest height of 100, so the distance between the bottom of that picture and the nail is equal to 60 + 100 = 160 cm.
the distance from the nail to the floor is 250 cm.
250 - 135.4 = 114.6 cm.
250 - 170 = 80 cm.
250 - 160 = 90 cm.
the picture that hangs closest to the floor would be the picture that is 120 cm wide and 90 cm high.
i believe that's going to be selection C.
here's a picture of the calculations for the longest height of each.
