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Answer :
You can translate the first sentence into an equation by using "w" and "L" for width and length, respectively. Note that the word "is" means an equals sign in "math language". Also, the phrase "7 inches less" means "subtract 7 from". Hence, the first sentence becomes: w= L-7 To find the second equation, you need to know the formula for the area of a rectangle. Area equals width times length. That means the second equation is A = w(L). We know that the area is 120, and we also know that w= L-7. That measn we can replace "A" with "120" and "w" with "L-7". We get: 120 = (L-7)(L) You'll need to multiply the two factors on the right hand side. The resulting equation will be quadratic, which means factoring or using the quadratic formula.
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Rewritten by : Barada
W=L-7
A=LW, using W from above you get:
A=L(L-7)
A=L^2-7L and A=120 so:
L^2-7L=120
L^2-7L-120=0
L^2-15L+8L-120=0
L(L-15)+8(L-15)=0
(L+8)(L-15)=0, since L>0
L=15in, and since W=L-7, W=8in
So length is 15 in and width is 8 in.
A=LW, using W from above you get:
A=L(L-7)
A=L^2-7L and A=120 so:
L^2-7L=120
L^2-7L-120=0
L^2-15L+8L-120=0
L(L-15)+8(L-15)=0
(L+8)(L-15)=0, since L>0
L=15in, and since W=L-7, W=8in
So length is 15 in and width is 8 in.
