Question

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?

Answer 1

Answer:

Answer on Edg is D

Step-by-step explanation:

just did the test

Answer 2

Answer

$(12+x)(15+x)=160+15*12$

Which simplifies to:

$x^2+27x-160=0$

Explanation

Let $x$ the number of feet they are going to expand the width and length of the patio. So the new width of the patio will be $12+x$ and the new length $15+x$.

Remember that the area of a rectangle is width times length, so the length of our expanded patio will be $(12+x)(15+x)$. But, we also know form our problem that they want to increase the total area of the patio by 160 ft2. The actual area of the patio is $(15ft)(12ft)$, so the expanded area of the patio will be $160ft^2+(15ft*12ft)$.

Now we can equate the expanded area of the patio and simplify:

$(12+x)(15+x)=160+15*12$

$180+12x+15x+x^2=160+180$

$180+27x+x^2=340$

$x^2+27x-160=0$