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Math Help - Another word problem that's stumping me

  1. #1
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    Another word problem that's stumping me

    This is yet another example of a problem on the sample NC EOG test (7th grade).

    A rectangular piece of land will be divided diagonally into two congruent triangular sections. One section will be covered with grass, and the other section will be paved. The blueprint measurements for the piece of land are 5 inches wide by 12 inches long. The blueprint scale is 1/4 inch = 10 feet. how much area will be paved.

    A) 2,400 square feet
    B) 9,600 square feet
    C) 48,000 square feet
    D) 96,000 square feet

    What steps do I take to find the answer to this?
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  2. #2
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    a quarter inch is 10 feet. How many quarter inches are 5 inches?. 20

    20*10=200 feet wide.

    How many quarter inches are in 12 inches?. 48

    48*10=480 feet long.

    The area of the rectangle is then (200)(480)=96,000

    Half of this is paving, 48,000

    Get out a rule and look at it. That may help.
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  3. #3
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    Quote Originally Posted by galactus View Post
    a quarter inch is 10 feet. How many quarter inches are 5 inches?. 20

    20*10=200 feet wide.

    How many quarter inches are in 12 inches?. 48

    48*10=480 feet long.

    The area of the rectangle is then (200)(480)=96,000

    Half of this is paving, 48,000

    Get out a rule and look at it. That may help.
    That makes perfect sense. You have no idea how grateful I am for your help. My daughter's test is this coming wed. and thurs. She failed 3 consecutive grading periods (18 weeks), and was then moved to another math class. Her grades have improved tremendously, but we're trying to work on things that she did before her class was changed. My brain feels like mush at this point.
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  4. #4
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    Quote Originally Posted by cherryperry View Post
    This is yet another example of a problem on the sample NC EOG test (7th grade).

    A rectangular piece of land will be divided diagonally into two congruent triangular sections. One section will be covered with grass, and the other section will be paved. The blueprint measurements for the piece of land are 5 inches wide by 12 inches long. The blueprint scale is 1/4 inch = 10 feet. how much area will be paved.

    A) 2,400 square feet
    B) 9,600 square feet
    C) 48,000 square feet
    D) 96,000 square feet

    What steps do I take to find the answer to this?
    Hi Cherry,

    if the rectangle is divided into 2 congruent (identical) rectangles,
    then both will have the same area which is equal to half the area of the rectangle.

    If 1/4 inch is 10 feet, then 1 inch represents 10(4) feet and so 5 inches represents 10(5)(4) feet = 200 feet.

    12 inches represents 12(4)(10)=480 feet

    The area of the rectangle is the number of "square feet" inside (like tiles)
    which is obtained by multiplying the side lengths.

    The triangle area is then half that figure.
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