Answer:
[tex]\huge\boxed{\sf Area = 12.8 cm\²}[/tex]
Step-by-step explanation:
Let,
The length of rectangle = x
The width of rectangle = y
The length of square = x - 4
The width of square = y + 5
Area of rectangle = xy
Area of square = xy + 40
Condition No. 1:
Area of Square = Length of square * Width of square
xy + 40 = (x - 4)(y - 5)
xy + 40 = xy - 5x - 4y + 20
- 5x - 4y = 40 - 20
- 5x - 4y = 20
5x + 4y = -20 ------------------(1)
Condition No. 2:
We know that:
Length of square = Width of square
x - 4 = y + 5
Add 4 to both sides
x = y + 5 + 4
x = y + 9 ---------------------------(2)
Solution:
Put Eq. (2) in (1)
5 (y + 9) + 4y = -20
5y + 45 + 4y = -20
9y + 45 = -20
9y = -20-45
y = -65 / 9
Now, Put the value of y in Eq. (2)
x = (-65 / 9) + 9
x = (-65 + 81) / 9
x = 16 / 9 cm
Now,
Area of rectangle = xy
Area = ( -65 / 9 ) * ( 16 / 9 )
Area = (-65*16) / (9*9)
Area = -1040/81
Area = 12.8 cm² (Neglecting -ve sign)
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
