Question 130827
P=2l+2w
64=2l+2w   substitute 64 for P

A=lw   substitute 240 for A
240=lw   Solve for either l or w.   I will solve for w.
w=240/l   Divide both sides by l

64=2l+2(240/l)   Substitution of (240/l) for w
64=(2l^2 +480)/l  find common denominator of l and combine like terms

64/1=(2l^2 +480)/l   Write the left side over 1 to form a proportion.
64=2l^2+480         Cross multiply

2l^2-64l+480 =0     Standard form of quadratic equation
2(l^-32l+240)=0       Factor out a common factor of 2
2(l-20)(l-12)=0       Factor the trinomial
l-20=0 and l-12=0     Set each variable factor equal to zero and solve each equation
l=20 and l-12        Let one answer be the width and one answer be the length
For example length = 20 and width =12