A rectangular plot of land with an area 60m²is fenced length of fencing being 100m. length of plot is
Answers
Step-by-step explanation:
Assuming that the plot of land is completely surrounded by fencing, the perimeter is 100 m100 m . Since the formula for a perimeter of a rectangle is P=2(l+w)P=2(l+w) , we have:
2(l+w)=1002(l+w)=100
So now we have a system of equations:
lw=600lw=600
2(l+w)=1002(l+w)=100
We can solve by elimination, substitution, or graphing. In this case, substitution is most likely the easiest.
We can divide the first equation by ll to get w=600lw=600l .
Then, we substitute 600l600l for ww :
2(l+w)=1002(l+w)=100
2(l+600l)=1002(l+600l)=100
Solving for ll , we get:
2(l+600l)=1002(l+600l)=100
l+600l=50l+600l=50
l2+600=50ll2+600=50l
l2−50l+600=0l2−50l+600=0
(l−30)(l−20)=0(l−30)(l−20)=0
l=30l=30 or l=20l=20
The width can either be 30 m or 20 m, depending on which side you decide is the length.
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