Question

The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width by 7 inches, the perimeter would be 160 inches. What is the width?

Answer 1

perimeter is
\[P=2l+2w\] and you know this is 6w so put
\[6w=2l+2w\]
\[4w=2w\]
\[2w=l\]

Answer 2

then put
\[2(l+4)+2(w+7)=160\]
\[2l+8+2w+14=160\]
\[2w+2l+22=160\]
\[2w+2l=138\]
\[w+l=69\] and since
\[l=2w\] this says
\[w+2w=69\]
\[3w=69\]
\[w=13\]

Answer 3

Back to the top. How did you get 4W=2W?

Answer 4

Solve the following for L and w:\[\{2L+2w=6w,2(L+4)+2(w+7)=160\}\]\[\{L=46,w=23\}\]First Equation: 2L+2w=6w
2*46 + 2*23 = 6*23 ?, 92 + 46 = 138 ?, 138 = 138 yes
Second Equation: 2 (L + 4) + 2 (w + 7) = 160
2*(46 + 4) + 2*(23 + 7) = 160 ?, 2*(50) + 2*(30) = 160 ?, 160 = 160 yes