Question

The sides of a triangular field are (3x2 – y2) units, (4x2 – 7xy + 4y2) units and ( -3x2 + 7xy + 8 y2) units. Find the perimeter of the field. If the cost of fencing the field per unit is Rs.11xy, find the total cost of fencing the entire field. ANS ACCORDING TO 8th GRADE PLS

Answer 1

★Answer :

• The perimeter of the triangular field is 5x² + 11y²

• The total cost of fencing the entire field is Rs. 55x² + 121y²

★Step-by-step explanation :

Given that,

The sides of a triangular field are (3x² – y²) units, (4x² – 7xy + 4y²) units and ( -3x² + 7xy + 8 y²) units.

We know that,

Perimeter of triangle = a + b + c

By putting the values,

Therefore, Perimeter of the field is :-

» (3x² – y²) + (4x² – 7xy + 4y²) + ( -3x² + 7xy + 8 y²)

» [ { 4x² + ( - 2x² ) + 3x² } + { ( - 7xy ) + 7xy } + { 4y² + 8y² + ( - y² ) } ]

Cancelling ( - 7xy ) and + 7xy

» [ { 4x² + ( - 2x² ) + 3x² } + { 4y² + 8y² + ( - y² ) } ]

» 5x² + 11y²

Therefore, perimeter of the field is 5x² + 11y²

Now, let's find the total cost of fencing the entire field

Given that, the cost of fencing the field per unit is Rs. 11xy

» ( 5x² + 11y² ) × ( 11xy )

» 55x² + 121y²

Therefore, total cost of fencing the entire field is Rs. 55x² + 121y²