Question 922719: if there is a rectangle that has an area of 45cm2 and a perimeter of 36cm what is its dimensions
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Area(A) of rectangle equals length(L) times width(W) or A=LW
Perimeter(P) of rectangle equals 2 times length(L) plus 2 times width(W) or P=2L+2W
Let L=length of rectangle
And let W=width of rectangle
2L+2W=36---eq1
L*W=45---eq2
from eq2, we see that L=45/W. Substitute this into eq1:
2(45/W)+2W=36 multiply each term by W:
2(45)+2W2=36W divide each term by 2
45+W2=18W or
W2-18W+45=0 quadratic in standard form and it can be factored
(W-15)(W-3)=0
so
W can equal 15ft or W can equal 3ft
If W=15 ft, we see from eq2 that L=3ft One possibility
If W=3ft, we see from eq2 that L=15ft The other possibility
Hope this helps---ptaylor
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