Work Step by Step
Step 1: Since it is given that the width, $w$, is 3 inches smaller than the length, $l$, and that the perimeter is 18 inches, we first solve for $l$ (length), using the formula $2l+2w$. Step 2: Plug the value for $w$ into the equation, getting $18=2l+2(l-3)$ Step 3: Distribute the 2: $18=2l+2l-6$ Step 4: Add 6 to both sides of the equation: $18+6=2l+2l-6+6$ Step 5: Simplify: $24=4l$ Step 6: Divide both sides of the equation by 4 to solve for $l$: $24\div4=4l\div4$ Step 6: $l=6$ Step 7: Now that you have found $l$, plug it back into the original equation, $18=2l+2w$, to solve for $w$: $w=6-3, w=3$ Step 8: Check your work by plugging both $w$ and $l$ into $18=2l+2w$. Then getting $18=18$. The width of the rectangle is 3 inches, the perimeter is 18 inches, and the length is 6 inches.