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8 September, 05:09

Triangle $ABC$ has sides of $6$ units, $8$ units, and $10$ units. The width of a rectangle, whose area is equal to the area of the triangle, is $4$ units. What is the perimeter of this rectangle, in units

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  1. 8 September, 07:53
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    20

    Step-by-step explanation:

    Given that the area of the rectangle is equal to that of the triangle

    Area of triangle $ABC$

    = 1/2 (bh)

    Given that the sides of the triangle are $6$ units, $8$ units, and $10$ units,

    The base and the heights are $6$ units and $8$ units. The $10$ units is the hypotenuse

    From Pythagoras theorem,

    6^2 + 8^2 = 10^2

    Therefore, area of triangle

    =1/2 (6 * 8)

    = $24$ units^2

    Area of rectangle = L * W

    Where L = Length, W = Width

    Area of the rectangle = area of triangle

    L * 4 = 24

    L = 24/4

    L = $6$ Units

    Perimeter of rectangle

    =2 (L + B)

    = 2 (6 + 4)

    = $20$ Units
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