how to solve The width of a triangle is one half its length. The perimeter of the rectangle is 54cm. What are the width and the length of the rectangle ?

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Do you mean the width of a rectangle is one half it's length? If so, 2W = L (1/2 of width is same as twice the length) 2W + 2L = 54 (formula for the perimeter of a rectangle) 2(1/2L) + 2L = 54 (substitude using your formula above about width 1/2 of length) L + 2L = 54 (simplify) 3L = 54 (simplify) L = 9 W = 18