The sum of the areas of two squares is 640m². If the difference of there perimeters is 64m,find the sides of the two squares?
Answers
Answered by
6
Answer:
8 m and 24 m
Step-by-step explanation:
Let the sides of the squares be x and y.
According to question,
x² + y² = 640 m²
4x - 4y = 64 m
=> x - y = 64m/4 = 16 m
=> x = 16 + y
Therefore,
(16 + y)² + y² = 640 m²
=> y² + 32y + 16² + y² - 640 = 0
=> 2y² + 32y + 256 - 640 = 0
=> 2y² + 32y - 384 = 0
=> y² + 16y - 192 = 0
=> y² + 24y -8y - 192 = 0
=> y( y + 24) - 8( y + 24) = 0
=> (y - 8)(y+24) = 0
y = 8 m (As y can't be negative(-24) )
x = 16 + y = 24 m
Similar questions