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masha68 [24]
3 years ago
13

A rectangle is three centimeters.longer than it is wide. if its length were to be decreased by two centimeters, its area would d

ecrease by thirty square centimeters.
A) what are the dimensions?
B) what is it’s area?
Show your work using an equation
Mathematics
1 answer:
Scorpion4ik [409]3 years ago
7 0
Given/equations formed from text:
I: l=w+3
II: A=l*w
III: new area B=(l-2)*w
IV: B=A-30

substitute l in II with I to remove l:
II': A=l*w=
(w+3)*w=
w^2+3w

substitute l in III with I to remove l:
III': B=(l-2)*w=
(w+3-2)*w=
(w+1)*w=
w^2+w

substitute A and B from II' and III' into IV:
B=A-30
w^2+w=w^2+3w-30
30=2w
w=15

insert w=15 into I:
l=15+3=18
->
A) dimensions of full size rectangle are width 15 and length 18
dimensions of reduced size rectangle are width 15 and length 16

B) full size: 15*18=10*18+5*18=180+90=270cm^2
reduced size: 15*16=10*16+5*16=160+80=240cm^2


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