sum of the areas of two squares is 850m^2. if the difference of their perimeter is 40m. find the sides of the two squares
Answers
HØLÁ...❤
_____________
Area of 1 square = a²
Area of 2 square = b²
It is given that ,
a² + b² = 850 m²
=> a² + b² = 850 ... (i)
Perimeter of 1 square = 4a
Perimeter of 2 square = 4b
4a - 4b = 40
4 ( a - b ) = 40
a - b = 10
a = 10 + b ....(ii)
Put value of a in (i)
a² + b² = 850
=> (10 + b)² + b² = 850
=> 100 + b² + 20b + b² = 850
=> 2b² + 20b = 750
=> 2b² + 20b - 750 = 0
=> 2 (b² + 10b - 375 ) = 0
=> b² + 10b - 375 = 0
=> b² + 25b - 15b - 375 = 0
=> b ( b + 25 ) - 15 ( b + 25 ) = 0
=> ( b + 25 ) ( b - 15 ) = 0
=> b = -25 or b = 15
Taking positive value of b = 15,
Putting the value of b in (ii)
a = 10 + b
=> a = 10 + 15
=> a = 25
Hence , the sides if two squares are 15 m and 25 m respectively.
Let 1 square be x
2 square be y
sum of the areas of two squares is 850m^2
x^2+y^2=850-----------(1)
difference of their perimeter is 40m
4x - 4y=40
x-y=10--------(2)
x=10+y
put the value of x in equation(1)
x^2+y^2=850
(10+y)^2+y^2=850
100+y^2+20y+y^2=850
2y^2+20y-750=0
y^2+10y-375
y^2+25y-15y-375=0
y(y+25) -15(y+25)
(y+25)(y-15)
y=15-------(3)
put the value of y in equation(2)
x=10+y
x=10+15
x=25
ThAnKs
❤️❤️ YoU