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.