Question

The davidson family wants to expand its rectangular patio, which currently measures 15 ft by 12 ft. they want to extend the length and width the same amount to increase the total area of the patio by 160 ft2. which quadratic equation best models the situation? a = lw (15)(12) (x)(x) = (15)(12) 160 (15x)(12x) = (15)(12) 160 2(15 x) 2(12 x) = (15)(12) 160 (15 x)(12 x) = (15)(12) 160

Answer 1

To model the Davidson family's patio extension with a quadratic equation, we use (15 + x)(12 + x) = 340. Expanding and rearranging leads to the equation x² + 27x - 160 = 0, which represents the problem accurately.

Step-by-step explanation:

The Davidson family wants to extend their rectangular patio that currently measures 15 ft by 12 ft. They plan to increase the total area by 160 ft2 by extending both the length and the width by the same amount, denoted as 'x'. The current area is 15 ft × 12 ft, which equals 180 ft2. The new area will be (15 + x) ft × (12 + x) ft. We can formulate a quadratic equation to model the situation:

• (15 + x)(12 + x) = 180 + 160
• (15 + x)(12 + x) = 340

Expanding the left side of the equation, we get:

• 15 × 12 + 15x + 12x + x2 = 340
• 180 + 27x + x2 = 340
• x2 + 27x + 180 = 340
• x2 + 27x - 160 = 0

This quadratic equation x2 + 27x - 160 = 0 best models the situation for the expansion of the patio.