Click an item in the list or group of pictures at the bottom of the problem and, holding the button

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. release your mouse button when the item is place. if you change your mind, drag the item to the trashcan. click the trashcan to clear all your answers. a circle has a radius of 6 in. the inscribed equilateral triangle will have an area of:

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  1. 6 √3

    Step-by-step explanation:

    Length of a side of an equilateral triangle inscribed in a circle =

    r

    3

    where r is the radius of the circle

    Therefore, Area =

    3

    a

    2

    4

    a

    =

    6

    3

  2. Let the third side of triangle be x

    Now parameter of triangle = sum of its sides

    Therefore,

    7a-11b=2a+b+a-9b+x

    4a-4b=x(ans.)

  3.   27√3 in² ≈ 46.765 in²

    Step-by-step explanation:

    There are several ways you can go at this. One is to recognize that the triangle formed by two vertices and the circle center is an isosceles triangle with apex angle 120°. Its area will be

      A = (1/2)·r²·sin(120°) = (1/2)·(6 in)²·(√3)/2 = 9√3 in²

    The total area of the inscribed triangle is the area of 3 of these, so is ...

      A = 3·9√3 in² = 27√3 in²

    ___

    Alternate solution

    If we call the center of the circle point O, and the vertices of the inscribed equilateral triangle A, B, and C, we can define point X on segment AB such that OX⊥AB.

    Triangle AOX is a 30°-60°-90° triangle, so has sides in the ratios 1 : √3 : 2. That is, AO is twice the length of OX, and AX is √3 times the length OX.

    This makes OX = 3, AX = XB = 3√3, and XC = OX+OC = 3+6 = 9.

    Now we have the dimensions of triangle ABC: the base AB is 6√3, and the height (XC) is 9. The area can be found in the usual way:

      A = 1/2·bh = 1/2·(6√3 in)·(9 in) = 27√3 in²

  4. Third side:4a-3b

    Step-by-step explanation:

    We know that perimeter of a triangle is sum of all three sides,i. e. x,y and z

    Here in the question

    x=2a+b

    y=a-9b

    and z=?

    P=7a-11b

    2a+b+a-9b+z=7a-11b

    3a-8b+z=7a-11b

    z=7a-11b-3a+8b

    z=4a-3b

    is the third side of the triangle.

    Hope it helps you.

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