Mathematical processes are the steps used to determine the result of operations
- The perimeter of the rectangle is [tex]10x^2 - 14x + 28[/tex]
- The area of the rectangle is [tex]5x^3 +17x^2 -31x + 45[/tex]
The dimension of the rectangle is given as:
[tex]Length = 5x^2 - 8x + 9[/tex]
[tex]Width = x + 5[/tex]
(1) The perimeter of the triangle
This is the sum of the side lengths of the rectangle.
So, we have:
[tex]Perimeter = 2 \times (Length + Width)[/tex]
This gives
[tex]Perimeter = 2 \times (5x^2 - 8x + 9 + x + 5)[/tex]
Collect like terms
[tex]Perimeter = 2 \times (5x^2 - 7x + 14)[/tex]
Open brackets
[tex]Perimeter = 10x^2 - 14x + 28[/tex]
Hence, the perimeter of the rectangle is [tex]10x^2 - 14x + 28[/tex]
(2) The area of the triangle
This is the product of the dimensions of the rectangle.
So, we have:
[tex]Area = Length \times Width[/tex]
This gives
[tex]Area = (5x^2 - 8x + 9) \times (x + 5)[/tex]
Open brackets
[tex]Area = 5x^3 - 8x^2 + 9x +25x^2 - 40x + 45[/tex]
Collect like terms
[tex]Area = 5x^3 - 8x^2 +25x^2+ 9x - 40x + 45[/tex]
[tex]Area = 5x^3 +17x^2 -31x + 45[/tex]
Hence, the area of the rectangle is [tex]5x^3 +17x^2 -31x + 45[/tex]
Read more about areas and perimeters at:
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