Anonymous asked in Education & ReferenceHomework Help · 1 decade ago

Can some1 help me with this math problem please??

1. the length of a rectangle is 4 times it width. if the area of the rectangle is 20 m (squared), find its length and width.

2. If the length of a rectangle is 4 more than its width and the area of the rectangle is 6in. (squared), find its length and width

6 Answers

  • 1 decade ago
    Favorite Answer

    1) L = 4W

    A = LW = 20

    Substitute L = 4W to get 20 = 4W x W

    20 = 4W^2, divide both sides by 4 to get

    5 = W^2, take square root of both sides to get W

    W = √5

    20 = L x W

    20 = L x √5, divide both sides by √5 to get L

    L = 20/√5 or, when rationalized, 4√5

    Final answer:

    L = 4√5 and W = √5


    2) L = W + 4

    A = 6 = L x W, substitute L = W + 4 to get

    6 = (W + 4) x W

    6 = W^2 + 4W, substract 6 from both sides to get

    0 = W^2 + 4W - 6

    This is not easily factored, so you'd have to use the quadratic equation to solve for W. Once you have W, just plug that in to L = W +4 to get the L value. Good luck!

  • glurpy
    Lv 7
    1 decade ago

    It's best to draw this out, which I can't do here. So draw yourself a rectangle. Your length is L (I would normally use a cursive lower case L to represent this because just using a lower case l can be confusing) and the width is w.

    What do you know about the length? We are told that it is 4 times the width. That means L=4*w which is the same thing as 4w, right?

    What do you know about the area of a rectangle?

    A=L * w or Lw

    Now if A=Lw, and we know that L=4w for this rectangle, that means that, for this rectangle:

    A=4w*w = 4w^2

    What else do we know about this rectangle? We know that its area is 20m^2. That means A=20m^2, or for simplicity, 20. Let's substitute that into the equation:


    Basic algebra: divide out the 4


    How do we solve w^2? To find w, we want to use the square root (sqrt). We have to do that to each side:

    sqrt5=sqrt (w^2)


    Now, since that 20 was actually m^2, the square root of the is m. So the w= sqrt5 meters

    As for the length, we know that the length is 4 times the width, which means that the length is 4(sqrt5) m.

    We then use our calculator to check if it works:

    A=4(sqrt5) * (sqrt 5)


    2. The length of a rectangle is 4 more than its width.

    What does that mean, exactly? Let's think about that, as I'm guessing that's where you are struggling:

    Let's say the width is this long -----. The length is 4 more than that ---------. So, that means the length is w+4, right?

    If A=L * w, and L = 2+4, then A = (w+4) * w.

    Hopefully you know how to work out the rest. Give it a shot and then post your answer and we can see if it's correct.

  • 1 decade ago

    1. Set Width = x and length = 4x

    Since the area of a rectangle is length times width set up your equation like 4x times x = 20 and solve

    2. Set width=x then length is x+4

    Set up the equation like before x times x+4 = 6 and solve

  • 1 decade ago

    1. since the length is 4 times the width, L = 4w

    Area = Lw

    Your area you gave is 20

    20 = (4w)(w)

    20 = 4w^2

    Divide both sides by 4

    5 = w^2

    Take the square root of both sides

    square root 5 = w

    Now you can put w = square root 5 into your L= 4w formula

    L = square root 5(2)

    L = 2 square root 5

    2. You have the length is 4 times its width, so L = 4w

    The area you have is 6

    Area = Lw

    6 = (4w)(w)

    6 = 4w^2

    Divide both sides by 4

    3/2 = w^2

    Take the square root of both sides

    w = square root 3/2

    Now but w = square root 3/2 into L = 4w

    L = 4(square root 3/2)

  • How do you think about the answers? You can sign in to vote the answer.
  • for a: do the following sollution:

    lenght is (x x4)m.

    width is (x)m.

    area is 21 m(squared)

    u put the numbers in the formulae of area= lengh x width.

    u will get x=2.5.

    then u place that in lengh: (x+4) which will be (2.5x4)=10.

    and do the same for width which is x= 2

    then i think the answer will be lengh is 10 and 2. i guess! just tried.

    for two:

    lenght is (x +4)m.

    width is (x)m.

    u put the numbers in the formulae of area= lengh x width.

    jsut work it out and do what i had done first by placing the value in lengh and in width! get it~??

  • 1 decade ago

    u hav 2 develop some equations inorder 2 solve this

    u can sub. 4 lenght as x and width as y

    and remember area is lenght times breadth

    sorry i dont hav enough time 2 do this 4 u

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