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
new length = 15+x
new width = 12+x
so the last one
h h
doodoo
The correct quadratic equation that best models the situation is:
(15 + x)(12 + x) = (15)(12) + 160
To understand how this equation is derived, let's break it down step by step:
1. Start with the formula for the area of a rectangle: A = lw (length times width).
2. The current patio dimensions are 15 ft by 12 ft, so the current area is (15)(12).
3. The family wants to extend both the length and width by the same amount (let's call it "x").
4. The new length and width will be (15 + x) and (12 + x), respectively.
5. The total area of the expanded patio will be the product of the new length and width: (15 + x)(12 + x).
6. Since the family wants to increase the total area by 160 ft², we add this value to the current area: (15)(12) + 160.
7. Combining all of the above, we arrive at the quadratic equation: (15 + x)(12 + x) = (15)(12) + 160.