Question

1. Use precise mathematical language to justify and explain each mathematical process.

Answer 1

Mathematical processes are the steps used to determine the result of operations

• The perimeter of the rectangle is $10x^2 - 14x + 28$
• The area of the rectangle is $5x^3 +17x^2 -31x + 45$

The dimension of the rectangle is given as:

$Length = 5x^2 - 8x + 9$

$Width = x + 5$

(1) The perimeter of the triangle

This is the sum of the side lengths of the rectangle.

So, we have:

$Perimeter = 2 \times (Length + Width)$

This gives

$Perimeter = 2 \times (5x^2 - 8x + 9 + x + 5)$

Collect like terms

$Perimeter = 2 \times (5x^2 - 7x + 14)$

Open brackets

$Perimeter = 10x^2 - 14x + 28$

Hence, the perimeter of the rectangle is $10x^2 - 14x + 28$

(2) The area of the triangle

This is the product of the dimensions of the rectangle.

So, we have:

$Area = Length \times Width$

This gives

$Area = (5x^2 - 8x + 9) \times (x + 5)$

Open brackets

$Area = 5x^3 - 8x^2 + 9x +25x^2 - 40x + 45$

Collect like terms

$Area = 5x^3 - 8x^2 +25x^2+ 9x - 40x + 45$

$Area = 5x^3 +17x^2 -31x + 45$

Hence, the area of the rectangle is $5x^3 +17x^2 -31x + 45$

Read more about areas and perimeters at:

brainly.com/question/15656646