The length and width of a rectangular patio are, (x + 8) feet and (x + 6) feet, respectively. if the area of the patio is 160 square feet, what are the dimensions of the patio?

can i have the work too?

Area of the rectangle(A) is given by:

where,

l is the length and w is the width of the rectangle.

As per the statement:

The length and width of a rectangular patio are, (x + 8) feet and (x + 6) feet, respectively. If the area of the patio is 160 square feet

⇒A = 160 square feet, l= x+8 feet and w = x+6 feet

then;

⇒

⇒

Subtract 48 from both sides we have;

Using completing square method:

⇒

⇒

Simplify:

Subtract 7 from both sides we have;

Since, the sides cannot be in negative;

⇒

Length of patio = feet

Width of patio = feet

Therefore, the dimensions of the patio are:

feet and feet

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.