Question 130076
Start with:
{{{A = L*W}}} Substitute A = 18.
1) {{{18 = L*W}}} and...
{{{P = 2L+2W}}} Substitute P = 18.
2) {{{18 = 2L+2W}}} Simplify to: {{{9 = L+W}}}
Rewrite equation 2) as:{{{L = 9-W}}} and substitute into equation 1) then solve for W.
{{{18 = (9-W)*W}}}
{{{18 = 9W-W^2}}} Rearrange to:
{{{W^2-9W+18 = 0}}} Factor.
{{{(W-3)(W-6) = 0}}}
{{{W = 3}}} or {{{W = 6}}}
Use the smaller value for W, so W = 3 and L = 9-W = 6
The solution:
The length is 6cm. and the width is 3cm.