The measurements of a rectangular plot of land with a perimeter of 70 km and an area of 300 km is 20 and 15.
Given that,
We have to find what are the measurements of a rectangular plot of land with a perimeter of 70 km and an area of 300 km.
We know that,
Let a and b be the side lengths of the rectangle
The perimeter is 70 km,
So, 2a+2b=70 equation(1)
The area is 300 km
So, a×b=380 equation(2)
To solve this system of 2 equations,
We express b in terms of a in eq 1 -> b=35-a
Then we substitute for b in eq 2 -> a×(35-a)=300
Some transformation leads to a²-35a+300=0
a²-20a-15a+300=0
a(a-20)-15(a-20)=0
(a-20)(a-15)=0
a=20,15
Now, substitute a in equation (1)
2a+2b=70
a+b=35
20+b=35
b=35-20
b=15
Now,
15+b=35
b=35-15
b=20
Therefore, the measurements of a rectangular plot of land with a perimeter of 70 km and an area of 300 km is 20 and 15.
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