Answer:
Length of the rectangle is either 0.5 units or 1.5 units.
Step-by-step explanation:
Given:
Perimeter of a unit square is equal to the perimeter of a rectangle.
Area of rectangle is 75 % of the square's area.
Unit square means a square of side length 1 unit.
So, perimeter of a unit square,
, is sum of all the 4 sides and is equal to:
![P_{s}=4\times 1=4](https://tex.z-dn.net/?f=P_%7Bs%7D%3D4%5Ctimes%201%3D4)
Therefore, perimeter of the rectangle is,
units.
Now, perimeter of rectangle of length
and width
is given as:
![P_{r}=2(l+b)](https://tex.z-dn.net/?f=P_%7Br%7D%3D2%28l%2Bb%29)
Therefore,
--------1
Again, area of a unit square is 1 square units.
So, area of rectangle 0.75 of 1 which is 0.75 square units.
Or,
--------2
Plug in
in equation 1, we get
![l+\frac{0.75}{l}=2\\l^{2}+0.75=2l\\l^{2}-2l+0.75=0\\(l-0.5)(l-1.5)=0\\l=0.5\textrm{ or } l=1.5](https://tex.z-dn.net/?f=l%2B%5Cfrac%7B0.75%7D%7Bl%7D%3D2%5C%5Cl%5E%7B2%7D%2B0.75%3D2l%5C%5Cl%5E%7B2%7D-2l%2B0.75%3D0%5C%5C%28l-0.5%29%28l-1.5%29%3D0%5C%5Cl%3D0.5%5Ctextrm%7B%20or%20%7D%20l%3D1.5)
![l=0.5 \textrm{ or }l= 1.5](https://tex.z-dn.net/?f=l%3D0.5%20%5Ctextrm%7B%20or%20%7Dl%3D%201.5)
Therefore, the length of the rectangle is 0.5 units or 1.5 units.