the perimeter of a rectangle is twice the sum of its length and its width. the perimeter is 46 meters and its length is 2 meters more than twice its width

Answer:The length of rectangle is 16 meters and the width of rectangle is 7 metersStep-by-step explanation:LetL -----> the length of the rectangleW ---> the width of the rectanglewe know thatThe perimeter of rectangle is equal to[tex]P=2(L+W)[/tex] ----> the perimeter of a rectangle is twice the sum of its length and its widthwe have[tex]P=46\ m[/tex]so[tex]46=2(L+W)[/tex]simplify[tex]23=(L+W)[/tex] -----> equation A[tex]L=2W+2[/tex] ----> equation Bsubstitute equation B in equation A and solve for W[tex]23=(2W+2+W)[/tex][tex]23=3W+2[/tex][tex]3W=23-2[/tex][tex]3W=21[/tex][tex]W=7\ m[/tex]Find the value of L[tex]L=2(7)+2=16\ m[/tex] thereforeThe length of rectangle is 16 meters and the width of rectangle is 7 meters