The width of a rectangle is 3/4 the length. the perimeter of the rectangle becomes 50 cm when the the length and the width are each increased by 3 cm. find the length and width

W= (3/4)l
2(l+3)+2(w+3)=50
multiply out
2l+6+2w+6=50
replace the w with the equation for w at the top and combine like terms
2l+2(3/4)l+12=50
multiply out
2l+3/2l+12=50
combine like terms and subtract 12 from both sides
7/2l=38
divide both sides by 7/2
l=76/7
find w
w=3/4l
w=(3/4)(76/7)
w=57/7
length= 76/7 or 10.86 cm
width= 57/7 or 8.14 cm