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Math Help - Please help me with this..(right triangle{geometry})

  1. #1
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    Please help me with this..(right triangle{geometry})

    1. A rectangle has a diagonal of 2 and length of √3. Find its width.

    2. Find the length of a side of a square with a diagonal of lenth 12.

    3. The perimeter of a rhombus is 40cm, and one diagonal is 12cm long. How
    long is the other diagonal?

    3. A diagonal of a square has lenth 8. What is the perimeter of the square?

    4. Find the altitude of an equilateral triangle if each side is 10 units long.

    *Please include the solutions....^^;;
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  2. #2
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    Quote Originally Posted by sarayork View Post
    1. A rectangle has a diagonal of 2 and length of √3. Find its width.

    2. Find the length of a side of a square with a diagonal of lenth 12.

    3. The perimeter of a rhombus is 40cm, and one diagonal is 12cm long. How
    long is the other diagonal?

    3. A diagonal of a square has lenth 8. What is the perimeter of the square?

    4. Find the altitude of an equilateral triangle if each side is 10 units long.

    *Please include the solutions....^^;;
    Hello,

    to 1.) A rectangle is divided into 2 congruent right triangles by one diagonal. The diagonal is the hypotenuse of the right triangle. If l is the length of the rectangle, w is the width and d is the diagonal then you have the equation:
    d^2 = l^2+w^2 . Plug in the values you know:

    2^2 = (\sqrt{3})^2 + w^2 and solve for w. (1)

    to 2.) A square is a special rectangle with l = w. Use the formula given above and solve for l:

    12^2 = 2 \cdot l^2.
    (6\sqrt{2})

    to 3.) A rhombus is divided by the 2 diagonals into 4 congruent right triangles where the side of the rhombus is the hypotenuse.
    length of one side: 10
    half of the given diagonal: 6

    If the half of the other diagonal is e (in Germany usually the diagonals are labeled e and f) then you get:

    10^2 = 6^2 + e^2 . Solve for e and calculate the complete length. (16)

    to 3.) again: If s is the length of one side of the square then the perimeter of a square is  p = 4 \cdot s. Calcualte the length of one side (same procedure as in #2.) and then the perimeter. (16\sqrt{2})

    to 4.) An equilateral triangle is divided into 2 congruent right triangles where the side of the triangle is the hypotenuse, one leg is the altitude and the other leg is the half of one side. Let h be the altitude then you have:

    10^2 = 5^2 + h^2 . Solve for h. \left(5 \cdot \sqrt{3}\right)
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