Question

The area of a rooftop can be expressed as 9x^2+6x+1. The rooftop is a quadrilateral.

Answer 1

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

∵ $\sqrt{9x^{2}}=3x$

∵ $\sqrt{1}=1$

∵ $(3x)(1)(2)=6x$

∴ 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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