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lukaswelker Rising GMAT Star Default Avatar
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area Post Thu Apr 17, 2014 8:42 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    Hello guys

    I'm going to far in calculations and I get it wrong. There must be an easier way.

    Here goes the question,

    A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

    19200 : 19600 : 20000 : 20400 : 20800.

    Please let me know if you see an easier way.

    Many thanks
    Lukas

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    theCodeToGMAT GMAT Titan
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    Post Thu Apr 17, 2014 9:14 am
    560 = 2 * (L + B)

    L + B = 280

    To find: L*B

    L^2 + B^2 = (200)^2
    (L+B)^2 -2*L*B = 200^2
    280^2 - 200^2 = 2 * L * B
    480 * 80 = 2 * L * B
    L * B = 19200

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    Post Thu Apr 17, 2014 9:26 am
    lukaswelker wrote:
    A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

    A) 19200
    B) 19600
    C) 20000
    D) 20400
    E) 20800.
    Let L and W equal the length and width of the rectangle respectively.

    perimeter = 560
    So, L + L + W + W = 560
    Simplify: 2L + 2W = 560
    Divide both sides by 2 to get: L + W = 280

    diagonal = 200
    The diagonal divides the rectangle into two RIGHT TRIANGLES.
    Since we have right triangles, we can apply the Pythagorean Theorem.
    We get L² + W² = 200²

    NOTE: Our goal is to find the value of LW [since this equals the AREA of the rectangle]

    If we take L + W = 280 and square both sides we get (L + W)² = 280²
    If we expand this, we get: L² + 2LW + W² = 280²
    Notice that we have L² + W² "hiding" in this expression.
    That is, we get: + 2LW + = 280²

    We already know that L² + W² = 200², so, we'll take + 2LW + = 280² and replace L² + W² with 200² to get:
    2LW + 200² = 280²
    So, 2LW = 280² - 200²
    Evaluate: 2LW = 38,400
    Solve: LW = 19,200 = A

    For extra practice, here's a similar question: http://www.beatthegmat.com/area-of-a-rectangle-t100119.html

    Cheers,
    Brent

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    osama_salah Just gettin' started! Default Avatar
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    Post Mon Jun 27, 2016 5:29 am
    How did you calculate 280² - 200² = 38,400 ?

    Brent@GMATPrepNow wrote:
    lukaswelker wrote:
    A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

    A) 19200
    B) 19600
    C) 20000
    D) 20400
    E) 20800.
    Let L and W equal the length and width of the rectangle respectively.

    perimeter = 560
    So, L + L + W + W = 560
    Simplify: 2L + 2W = 560
    Divide both sides by 2 to get: L + W = 280

    diagonal = 200
    The diagonal divides the rectangle into two RIGHT TRIANGLES.
    Since we have right triangles, we can apply the Pythagorean Theorem.
    We get L² + W² = 200²

    NOTE: Our goal is to find the value of LW [since this equals the AREA of the rectangle]

    If we take L + W = 280 and square both sides we get (L + W)² = 280²
    If we expand this, we get: L² + 2LW + W² = 280²
    Notice that we have L² + W² "hiding" in this expression.
    That is, we get: + 2LW + = 280²

    We already know that L² + W² = 200², so, we'll take + 2LW + = 280² and replace L² + W² with 200² to get:
    2LW + 200² = 280²
    So, 2LW = 280² - 200²
    Evaluate: 2LW = 38,400
    Solve: LW = 19,200 = A

    For extra practice, here's a similar question: http://www.beatthegmat.com/area-of-a-rectangle-t100119.html

    Cheers,
    Brent

    Post Mon Jun 27, 2016 5:32 am
    osama_salah wrote:
    How did you calculate 280² - 200² = 38,400 ?
    Aside: 28² = 784, which means 280² = 78,400

    So, 280² - 200² = 78,400 - 40,000
    = 38,400

    _________________
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    Use our free video course along with Beat The GMAT's free 60-Day Study Guide

    Thanked by: osama_salah
    GMAT Prep Now's 35-hour (500+ videos) course is 100% FREE. Use our free course in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

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