Find the side of the rectangle whose perimeter is 100 meters and area 600sq. Meters
Answers
Step-by-step explanation:
Let’s dissect this problem one part at a time.
A rectangular plot of land with an area of 600 metre squared is fenced
Okay, that’s self-explanatory. The formula for the area of a rectangle is A=lb , with l being the length and w being the width. Since the area is 600 m2 , the equation turns into:
lb=600
length of fencing being 100 m. Find the length of the plot?
Assuming that the plot of land is completely surrounded by fencing, the perimeter is 100 m . Since the formula for a perimeter of a rectangle is P=2(l+b) , we have:
2(l+b)=100
So now we have a system of equations:
lb=600
2(l+b)=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 l to get b=600l .
Then, we substitute 600l for b :
2(l+b)=100
2(l+600l)=100
Solving for l , we get:
2(l+600l)=100
l+600l=50
l2+600=50l
l2−50l+600=0
(l−30)(l−20)=0
l=30 or l=20
The width can either be 30 m or 20 m, depending on which side you decide is the length.