Geometry Right triangles and triangles problem please help me?

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  • 2 months ago

     What is the exact side length of a square 

     that has a diagonal length of 12 cm? 

     Diagonal = 12 cm

     Diagonal of a square is √2 x length of the side 

     √2 x side = 12 

     side = 12 / √2 

     √2 = 1.414 

     side = 12 / 1.414 = 8.4865...cm

  • 2 months ago

    1.  x=sqrt(144/2)= 8.48528 cm

    2. s=6/ sin 60=6.92841

    3. f=sqrt(2500+2500)=71+100=171 ft.

  • 2 months ago

    If you have a square that you cut in half with a diagonal you create two right triangles with the same dimensions.  This diagonal length becomes the hypotenuse.

    So we can use the Pythagorean Theorem to find the length of the other two sides:

    a² + b² = c²

    Since this is a square, a and b are equal (will set them to x) and c is given as 12 cm:

    x² + x² = 12²

    2x² = 144

    x² = 72

    x = √72

    x = √(36 * 2)

    x = 6√2 cm

    ----------------

    For the second one, this is an equilateral triangle where you are given the height.  The height cuts the base in half so the base of the smaller right triangles are half the size of the hypotenuse.

    Using the same equation we can solve for the length of the sides of the triangle, using:

    a = x/2

    b = 6

    c = x

    We get:

    a² + b² = c²

    (x/2)² + 6² = x²

    x²/4 + 36 = x²

    36 = x² - x²/4

    common denominator:

    36 = 4x²/4 - x²/4

    36 = (4x² - x²)/4

    36 = 3x²/4

    Multiply both sides by (4/3):

    48 = x²

    x = √48

    x = √(16 * 3)

    x = 4√3 cm

    ---------------

    The last one gives you a 45-45-90 triangle like the first one with one given side.  This means the other side is the same.  We can solve for the unknown hypotenuse, again, with the same equation:

    a² + b² = c²

    50² + 50² = c²

    2500 + 2500 = c²

    5000 = c²

    c = √5000

    c = √(2500 * 2)

    c = 50√2 ft

    The question asks for the perimeter so add the lengths of the three sides:

    a + b + c

    50 + 50 + 50√2

    (100 + 50√2) ft

    You are asked to round to the nearest foot, so:

    171 ft

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