Question

A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all
around it having an area of 120 m². Form the quadratic equation.​

Answer 1

Answer:

x = 2

Step-by-step explanation:

PQRS= rectangular field

ABCD= outer rectangle

1 : Length of rectangle  PQRS = l = PQ= 16m

Breadth = b = QR= 10m

Width = xm

Length of rectangle ABCD = I' = AB= 16 +2x

breadth = b' = CD= 10+ 2x

2 : Length of rectangular field PQRS= l = 16

Breadth = b = 10

Area of rectangle PQRS = l x b = 160

Area of rectangle ABCD= l' x b' = (16+2x) (10+2x) = 4x² +52x + 160

3 : area of path = area of PQRS = area of ABCD 

= 4x² +52x + 160 - 160 

= 4x²+ 52x

4 : Area of path = 120

so, 120 = 4x²+ 52x

∴ x= 2 and ∴ x= -15 

-15 will be rejected as length cannot be negative.

Therefore, x = 2