Part A: The type of the quadrilateral of the rooftop is a square
Part B: The length of one side of the rooftop is 19 m
Step-by-step explanation:
Let us revise some notes about quadratic expression
- (a + b)² = a² + 2ab + b², where a² + 2ab + b² is a perfect square trinomial because it gives square binomial (a + b)²
- Area of a square can be represented by perfect square trinomial, where the side of the square represented by the binomial
The area of a rooftop can be expressed as 9x² + 6x +1
The rooftop is a quadrilateral
We need to find the type of the quadrilateral and the length of
one side of the rooftop
∵ The area of the rooftop = 9x² + 6x +1
- Check if 9x² + 6x +1 is a perfect trinomial
∵ [tex]\sqrt{9x^{2}}=3x[/tex]
∵ [tex]\sqrt{1}=1[/tex]
∵ [tex](3x)(1)(2)=6x[/tex]
∴ 9x² + 6x +1 = (3x + 1)²
∴ 9x² + 6x +1 is a perfect square trinomial
∵ Perfect square trinomial can represent the area of a square
∴ The quadrilateral is a square
Part A: The type of the quadrilateral of the rooftop is a square
∵ The area of the rooftop is 9x² + 6x +1
∵ 9x² + 6x +1 = (3x + 1)²
∵ Area of the rooftop = 361 m²
∴ (3x + 1)² = 361
- Take square root for both sides
∴ 3x + 1 = 19
∵ The area of a square = (side)²
∵ The area of a square = (3x + 1)²
∴ 3x + 1 is the length of the side of the square
∵ 3x + 1 = 19
∴ The length of the side of the square is 19 m
Part B: The length of one side of the rooftop is 19 m
Learn more:
You can learn more about perfect square trinomial in brainly.com/question/7932185
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