The width of a triangle is two thirds its length. If the perimeter is 180 metres, find the dimensions of the rectangle.
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The perimeter of the rectangle is calculated by the formula [ 2(length +width) ] and as given in the data it is 180 metres.
Now equate everything,
2(2/3x +x) =180
2/3x +x =180/2
2/3x +x = 90
Now take x as a common variable on the L.H.S.
x(2/3 +1) =90
Add 2/3 and 1 on the L.H.S,
x(5/3) = 90
x = 90 / (5/3)
x = 90 * 3/5
x = 54
Therefore, the length of the rectangle is 54 metres and the width is 36 metres(2/3 of 54)
Now equate everything,
2(2/3x +x) =180
2/3x +x =180/2
2/3x +x = 90
Now take x as a common variable on the L.H.S.
x(2/3 +1) =90
Add 2/3 and 1 on the L.H.S,
x(5/3) = 90
x = 90 / (5/3)
x = 90 * 3/5
x = 54
Therefore, the length of the rectangle is 54 metres and the width is 36 metres(2/3 of 54)
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