a rectangular field is 70 m long and 50 m wide, has an uniform width path around it. If the path is 1024 m2 find the width of the path.
Answers
Answered by
85
Area of field = 70 X 50 = 3500 m²
Area of path = 1024 m²
ADD = 4524m²
Let the width be x meters
( 70+2x) ( 50+2x) = 4524
3500 + 100x +140x + 4x² = 4524
4x² + 240x - 1024 = 0
Dvide by 4
x² + 60x - 256= 0
x² +60x = 256
add 900
x² +60x +900 = 1156
( x+ 30)² = 1156
x = \/1156 - 30 = 34-30 = 4 meters is the answer
Area of path = 1024 m²
ADD = 4524m²
Let the width be x meters
( 70+2x) ( 50+2x) = 4524
3500 + 100x +140x + 4x² = 4524
4x² + 240x - 1024 = 0
Dvide by 4
x² + 60x - 256= 0
x² +60x = 256
add 900
x² +60x +900 = 1156
( x+ 30)² = 1156
x = \/1156 - 30 = 34-30 = 4 meters is the answer
anonymous12345:
Why 2x?
Similar questions