Question

area of the path of around a square field is 425 m square . find the width of the path if the side of the square is 40m . it's answer is 6162.25 m square ​

Answer 1

Step-by-step explanation:

→ Area of path = Area of region

Area of path = Area of region(1),(2),(3),(4)

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2 −1.6w+25=0

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2 −1.6w+25=0⇒40w

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2 −1.6w+25=0⇒40w 2

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2 −1.6w+25=0⇒40w 2 −16w+250=0

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2 −1.6w+25=0⇒40w 2 −16w+250=0⇒20w

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2 −1.6w+25=0⇒40w 2 −16w+250=0⇒20w 2

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2 −1.6w+25=0⇒40w 2 −16w+250=0⇒20w 2 −8w+125=0

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2 −1.6w+25=0⇒40w 2 −16w+250=0⇒20w 2 −8w+125=0D=8

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2 −1.6w+25=0⇒40w 2 −16w+250=0⇒20w 2 −8w+125=0D=8 2

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2 −1.6w+25=0⇒40w 2 −16w+250=0⇒20w 2 −8w+125=0D=8 2 −4(20)(125)<0

Area of path = Area of region(1),(2),(3),(4)⇒25=(0.4+2w)w×2+(0.4)w×2⇒25=0.8w−4w 2 +0.8w⇒4w 2 −1.6w+25=0⇒40w 2 −16w+250=0⇒20w 2 −8w+125=0D=8 2 −4(20)(125)<0⇒ No solution

Answer 2

Answer:

Area of path = 4x^2+4(40x)

Where x is the width of the path

4x^2 +160x=425

4x^2+160x-425=0

4x^2+170x-10x-425=0

4x(x+42.5)-10(x+42.5)=0

4x=10 and x =-42.5

X=2.5 path cant be negative

So path width 2.5 m