Bobby knows that the perimeter of the original rectangle is 120 meters. He also knows that the perimeter of the reduced rectangle is 30 meters and the reduced length is 9 meters.

The question isWhat are the dimensions of the original rectangle?Step 1Find the scale factorwe know thatThe scale factor is equal to[tex]scale\ factor=\frac{Perimeter\ original \ rectangle}{Perimeter\ reduced\ rectangle}[/tex]we have[tex]Perimeter\ original \ rectangle=120\ m[/tex][tex]Perimeter\ reduced \ rectangle=30\ m[/tex]Substitute the values[tex]scale\ factor=\frac{120}{30}=4[/tex]thereforethe scale factor is [tex]4[/tex]Step 2Find the width of the reduced rectanglewe know thatThe perimeter of a rectangle is equal to[tex]P=2L+2W[/tex]whereL is the length side of the rectangleW is the width side of the rectangleReduced rectanglewe have[tex]L=9\ m[/tex][tex]P=30\ m[/tex]substitute[tex]30=2*9+2W[/tex][tex]30=18+2W[/tex]Solve for W[tex]2W=30-18[/tex][tex]W=12/2=6\ m[/tex]thereforeThe dimensions of the reduced rectangle are [tex]9\ m\ *\ 6\ m[/tex]Step 3Find the dimensions of the original rectangleOriginal Lengthwe know that[tex]original\ length=scale\ factor*reduced\ length[/tex]we have[tex]reduced\ length=9\ m[/tex][tex]scale\ factor=4[/tex]substitute[tex]original\ length=4*9=36\ m[/tex]Original Widthwe know that[tex]original\ width=scale\ factor*reduced\ width[/tex]we have[tex]reduced\ width=6\ m[/tex][tex]scale\ factor=4[/tex]substitute[tex]original\ width=4*6=24\ m[/tex]thereforeThe dimensions of the original rectangle are [tex]36\ m\ *\ 24\ m[/tex]