Suki used a 10 foot length of fencing as two sides of the border of a triangle garden as shown above, where a wall is the third side of the border. if the side of the fence perpendicular to the wall is x feet long, what is the length, in feet, of the side of the border formed by the wall?

10-2x
10+2x
100-20x (all under square root thing)
100-20x+ x^2 (also under square root)

Remember that, by the Pythagorean's theorem, in a triangle rectangle the sum of the squares of the catheti is equal to the square of the hypotenuse.

Using that and the given information we can find that the length of the side of the border formed by the wall is:

L = √(100ft^2 - 20ft×x)

We know that we have one side perpendicular to the wall, then the angle between these two is equal to 90°, which means that these two are the catheti.

We also know that:

The length of the catheti perpendicular to the wall is x.

The total length of fencing is 10ft.

Then the length of the last side, the hypotenuse, is 10ft - x.

Now we want to find the length of the side that is along the wall, which we will call L.

Then using the Pythagorean's theorem we can write:

L^2 + x^2 = (10ft - x)^2

Solving for L, we get;

L^2  = (10ft - x)^2 - x^2

L^2 = 100ft^2 - 2×10ft×x + x^2 - x^2

L^2 = 100ft^2 - 20ft×x

L = √(100ft^2 - 20ft×x)

Then we can see that the correct option is the third one.

If you want to learn more, you can read:

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10+2x is the answer

The correct sentence is B : They haven't found anyone to help with the decorations.

All of the other sentences have double negatives.
For instance, in A: never and nobody are both negatives. The correct sentence should be: The large man would never hurt anybody.

C: didn't and nothing. Sharon insists she didn't know anything about her surprise party.

D: hasn't and none. Lance hasn't started any of his homework so far.