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Math Help - Problem Solving Using Quadratic Equations

  1. #1
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    Problem Solving Using Quadratic Equations

    Hi,

    I'm having a hard time answering these.

    Please help.

    Thanks in advance.
    ___________________________________________

    1. Find the dimensions of a right triangle if the area is 120 square units and one leg is more than twice the other leg.

    2. The area of two squares is 117 square centimeters. Their perimeter is 60 centimeters. Find the length of a side of each square.

    3. The sum of the radii of two circles is equal to 17 centimeters. The sum of the areas of these two circles equals the area of a circle whose radius is 13 centimeters. Find the radii.

    4. The difference between a number and its reciprocal is 7/12. Find the number.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Hi888 View Post
    1. Find the dimensions of a right triangle if the area is 120 square units and one leg is more than twice the other leg.
    Always start in the same place - Name Stuff!

    L = Length of the Shorter Leg of the Right Triangle
    W = Length of the Longer Leg of the Right Triangle

    Then translate:

    "the area is 120 square units"

    ˝LW = 120

    "one leg is more than twice the other leg"

    W > 2*L

    "Find the dimensions of a right triangle" [emphasis added]

    It doesn't specify a particular triangle. Just pick one.

    W = 3*L maybe.
    W = 2*L + 1 maybe
    W = \pi \cdot L maybe.

    Share your work. Let's see what you get.
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  3. #3
    Member maybeline9216's Avatar
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    Quote Originally Posted by Hi888 View Post
    Hi,

    I'm having a hard time answering these.

    Please help.

    Thanks in advance.
    ___________________________________________

    1. Find the dimensions of a right triangle if the area is 120 square units and one leg is more than twice the other leg.

    2. The area of two squares is 117 square centimeters. Their perimeter is 60 centimeters. Find the length of a side of each square.

    3. The sum of the radii of two circles is equal to 17 centimeters. The sum of the areas of these two circles equals the area of a circle whose radius is 13 centimeters. Find the radii.

    4. The difference between a number and its reciprocal is 7/12. Find the number.
    For qn1) wat is leg??wad do u mean by dat? Is it the length??

    2) Let the length of one square be x cm
    Let the length of another square be y cm.

    Perimeter means to add up all the sides of a square.
    So Total perimeter= 4x + 4y
    Therefore, 4x+4y=60 -(eqn 1)
    From (1): 4(x + y)=60
    ( x+y)=15
    x= 15-y -(eqn 1)

    To find area of a square, simply multiply the 2 sides of the square(Length X Breadth)

    So, total area of the 2 squares=x^2 + y^2

    Therefore, x^2 + y^2 = 117 -(eqn 2)

    Sub eqn(1) into eqn(2):

    (15-y)^2 + y^2= ? (continue on ur own)
    Then sub the value of y into either eqn(1) or eqn(2) to get the value of x...

    3) Let radius of 1st circle be x cm
    Let radius of 2nd circle be y cm.

    Sum of radius means to add x and y together.
    So, x+y=17
    x=17-y -eqn(1)

    Area of circle=(pi)r^2

    So, area of the 2 circles=(pi)x^2 + (pi)y^2

    [The sum of the areas of these two circles equals the area of a circle whose radius is 13 centimeters.]

    This statement means that (pi)x^2 + (pi)y^2 = (pi) 13^2
    (pi) (x^2 + y^2) =(pi) 169
    Therefore, (x^2 + y^2) = 169 -eqn(2)
    Sub eqn (1) into eqn(2) and so on....

    4) Let the number be x.
    Reciprocal of the number= 1/x
    Difference between them = x - 1/x
    So, x - 1/x = 7/12
    Continue on ur own.....

    I think ur problem is dat u are not sure how to construct the equations in order to find the answer....just read the question carefully and do things step by step...=)
    Last edited by maybeline9216; October 7th 2008 at 08:22 AM. Reason: sign inputed wrongly
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