Respuesta :
The area of the field where the length of each side is increased by 10% is 48.4 [tex]cm^{2}[/tex].
Step-by-step explanation:
The given is,
A rectangle field has an area of 40 [tex]cm^{2}[/tex]
If one side of the field is 3 cm longer than the other side
The length of new area in each side is increased by 10%
Step:1
Let,
[tex]b[/tex] - One side of rectangle
[tex]l[/tex] - Other side of rectangle
From given.
[tex]l[/tex] - [tex]b[/tex] +3
Formula for area of rectangle,
[tex]Area, a = lb[/tex]
40 = ( b+3) × b
40 = [tex]b^{2}[/tex] + 3b
Solving the above the equation,
b = 5 cm
l = 8 cm
Step:2
If the area of rectangle increased by 10%,
l = 8 + ( 8 × [tex]\frac{10}{100}[/tex] )
= 8.8
b = 5 + ( 5 × [tex]\frac{10}{100}[/tex] )
= 5.5
Area of rectangle is,
a = ( 8.8 × 5.5 )
= 48.4 square centimeters
Result:
The area of the field where the length of each side is increased by 10% is 48.4 [tex]cm^{2}[/tex], if a rectangle field has an area of 40 square centimeters and one side of the field is 3 cm longer than the other side.
