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The width of a rectangle is three fourths the length. The perimeter of the rectangle becomes 50 cm when the length and the width are each increased by 2cm. Find the length and the width.

Draw a diagram and convince yourself that the perimeter P=2(L+W)
We're told that W=(3/4)L.
We're also told that P=50 when W+2 and L+2 are used. So
50=2((L+2) + (W+2))=2((L+2) + ((3/4)L + 2))
25=(L + (3/4)L + 4)
Solve for L then use the relation between W and L given above, i.e. the first sentence of the problem.

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