Trey's mom planted an 18 feet by 20 feet garden in his back yard. this new garden reduced the area of trey's backyard by 24%. which answer choice best represents the total area of the back yard

The garden area is given by:

We are looking for the backyard area now.

For this, we make the following rule of three:

360 ---------------------> 24%

x -------------------------> 100%

From here, we must clear the value of x.

We have then:

The total area of the back yard is:

First find the missing length of the left triangle with the pythagorean theorem a² + b²= c² → 4² + 6² = c² → 16 + 36 = c² → 52 = c² → √52 = c

Now if you turn your head you can see a right triangle made of the two smaller triangles. The √52 is one of the legs. We know that the hypotenuse is 6 + y so we can substitute these values into the pythaorean theorem as well to find the blank side length of the smaller triangle to the right.

√52² + b² = (6 + y)² → 52 + b² = (6 + y)(6 + y) I know this seems like a lot but this is how I'd do it. You need to multiply (foil method) the (6+y)(6+y) to get 36 + 6y + 6y + y² which simplifies to 36 + 12y + y². Here's what we have: to find the hypotenuse of the smaller triangle to the right we need to simplify 52 + b² = 36 + 12y + y²; subtract 52 from both sides

b² = y² + 12y - 16 (I rearranged to make it easier to see); square root both sides

b = this is the hypotenuse of the smaller triangle to the right

Then we can use the pythagorean theorem for the small triangle to the right to eventually find the value of y.

4² + y² = ²

16 + y² = y² + 12y - 16; now solve, add 16 to both sides

32 + y² = y² + 12y; subtract y² from both sides

32 = 12y; divide both sides by 12

approximately 2.6 = y but since it says do not approximate, I would put y = 32/12

I hope that helps!!!

Ignore the weird A under the radical, I don't know why that's there. It's supposed to be just y²