Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

Simple Geometry. Find x.?

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  • 4 weeks ago
    Best Answer

    First, if the sides are x, we can agree the pink shape is a square. Its diagonal will be x√2

    If this isn't clear, use the Pythagorean Theorem:

    d² = x² + x²

    d² = 2x²

    d = √(2x²)

    d = (√2)x

    d = x√2

    Now look what we can do in the diagram below. We can extend the bottom line by 9 more to make it 23. Then add a perpendicular line of 7 units. You have now formed a right triangle with legs of 7 and 23. The hypotenuse is also the diagonal of the square.

    d² = 7² + 23²

    d² = 578

    d = √578

    d = √289 * √2

    d = 17√2

    We can easily see that x = 17

    d = x√2

    d = 17√2

    Hence:

    x = 17

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  • JOHN
    Lv 7
    4 weeks ago

    Let u = ∠ length 14 segment makes with side of square.

    Vertical side x has 3 parts:

    x = 14sinu + 7cosu + 9sinu = 23sinu + 7cosu

    Horizontal side x has 3 parts:

    x = 14cosu + 7sinu + 9cosu = 23cosu + 7sinu

    23sinu + 7cosu = 23cosu + 7sinu

    16sinu = 16cosu

    tanu = 1 (0 < u < 90)

    u = 45

    x = (23 + 7)/ √2 = 15√2.

  • 4 weeks ago

    A diagonal.from upper right to lower left will form two similar right triangles with sides 14, y, √(196 + y^2) and 9, 7-y, √(81 +(7-y)^2)

    14/y = 9/(7-y)

    98 -14y = 9y

    y = 98/23

    Should be easy from there since both sides are the same.

  • Anonymous
    4 weeks ago

    I have no exes..........

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  • Mark
    Lv 7
    4 weeks ago

    If it's so simple, then why don't you do it yourself? I'll give you a hint: think right triangle and the Pythagorean Theorem.

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