The perimeter of square a is 28 feet less than the perimeter of square b. the area of square a is 161 square feet less than the area of square b. if x and y are the side lengths of square a and square b, respectively, what is the value of x + y?

X+y=23.

The equation comparing the areas of the squares would be:

x²=y²-161

This is because the area of a square is found by multiplying its length and width; if x is the length of the smaller square, and y is the length of the larger square, we know that x*x, the area of the smaller square, is 161 less than y*y, the area of the larger square.

The equation comparing the perimeters of the squares would be:

4x=4y-28

This is because the perimeter is found by adding all of the sides; x+x+x+x=4x.  Similarly, y+y+y+y=4y; however, the perimeter of the smaller square is 28 less than 4y.

Using the equation for the perimeters, we can isolate x.  Divide both sides by 4:

4x/4 = 4y/4 - 28/4
x=y-7

Now we can substitute this into the equation for area:
(y-7)²=y²-161
(y-7)(y-7)=y²-161

Multiplying the binomials on the left we have:
y*y-7*y-7*y-7(-7)=y²-161
y²-7y-7y+49=y²-161
y²-14y+49=y²-161

We cannot have a variable on both sides; subtract y² from each:
y²-14y+49-y²=y²-161-y²
-14y+49= -161

Subtract 49 from both sides:
-14y+49-49 = -161-49
-14y = -210

Divide both sides by -14:
-14y/-14 = -210/-14
y=15

Substitute this back into the perimeter equation:
4x=4(15)-28
4x=60-28
4x=32

Divide both sides by 4:
4x/4=32/4
x=8

Therefore x+y=8+15=23.

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.