SOLUTION: Please help me solve this equation: the perimeter of a rectangle is 64 cm.the area is 240cm^2. what are its dimension?

Question 130827This question is from textbook
: Please help me solve this equation: the perimeter of a rectangle is 64 cm.the area is 240cm^2. what are its dimension? This question is from textbook

Answer by cngriffith(27) (Show Source): You can put this solution on YOUR website!
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

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