Helena creates two similar rectangles using exactly 100 cm of string. The smaller rectangles width and length are 4 cm by 6 cm respectfully. What are the dimensions of the larger rectangle? Rounded to the nearest whole number.

Answer:The dimensions of the larger rectangle are [tex]24\ cm[/tex] of length by [tex]16\ cm[/tex] of widthStep-by-step explanation:Letx-----> the length of the larger rectangley-----> the width of the larger rectanglewe know that[tex]\frac{x}{y}=\frac{6}{4}[/tex] ------> by similar rectangles[tex]x=1.5y[/tex] -----> equation AFind the perimeter of the smaller rectangle[tex]P=2(6+4)=20\ cm[/tex]Find the perimeter of the larger rectangleSubtract  the perimeter of the smaller rectangle from 100 cm of string[tex]P=100-20=80\ cm[/tex]Remember that[tex]80=2x+2y[/tex] ------> [tex]40=x+y[/tex] ------> equation Bsubstitute equation A in equation B[tex]40=1.5y+y[/tex] [tex]2.5y=40[/tex] [tex]y=16\ cm[/tex] Find the value of x[tex]x=1.5(16)=24\ cm[/tex]The dimensions of the larger rectangle are [tex]24\ cm[/tex] of length by [tex]16\ cm[/tex] of width