Answer:
The dimensions of the larger rectangle are [tex]24\ cm[/tex] of length by [tex]16\ cm[/tex] of width
Step-by-step explanation:
Let
x-----> the length of the larger rectangle
y-----> the width of the larger rectangle
we know that
[tex]\frac{x}{y}=\frac{6}{4}[/tex] ------> by similar rectangles
[tex]x=1.5y[/tex] -----> equation A
Find the perimeter of the smaller rectangle
[tex]P=2(6+4)=20\ cm[/tex]
Find the perimeter of the larger rectangle
Subtract 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 B
substitute 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
