Hello Addie,

We know that the width of the rectangle is unknown - this will be our variable x

We know that the length is 8 more than the width - the expression x + 8 represents the length

From what you told us, we are to take 4 inches from the length and then add it to the width.

This gives us a square because we now have a rectangle that measures x +4 in length and x + 4

in width. You also said that the area of the new square is 275.56 in^{2}. The formula for area looks

like this

275.56 = (x + 4)(x + 4) the next thing that we do is foil the right side.

275.56 = x^{2} +4x + 4x + 4*4 simplify and combining like terms give

275.56 = x^{2} + 8x + 16 at this point we want to bring the 275.56 over to the right side of the equation

0 = x^{2} + 8x + -259.56 in this form, we can use the quadratic formula to solve for x

x = (-b + sqrt(b^{2} - 4ac))/2a

x = (-8 + sqrt(8^{2} - 4 (1)(-259.56)))/2

x = 12.6

Now that we know what x equals, we can go back and substitute it into the original expression. When we do that we get 12.6 + 8 = 20.6 for the length, and 12.6 for the width.

I hope this helps.

Ishmael Patterson

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