I believe that the answer to that one would be A.
Answer:
x = -5
Step-by-step explanation:
Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.
This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).
So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.
On the right side we are given 9 for AD, and 18 for DC.
9/18 = 0.5
This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:
If AD/DC = 0.5, then BE/EC will also = 0.5
BE = x+23
EC = x+41
Therefore:

Now we can solve by multiplying both sides by x+41 to eliminate the fraction:

Now we multiply out the brackets and move the terms to different sides:



And if we substitute the -5 into the equations:
-5+23 = 18
-5 + 41 = 36
We will see that -5 does indeed give us the same ratio between the lengths:
18/36 = 0.5
Hope this helped!
Answer:
the correct answer is the 3rd one
Let the side of the garden alone (without walkway) be x.
Then the area of the garden alone is x^2.
The walkway is made up as follows:
1) four rectangles of width 2 feet and length x, and
2) four squares, each of area 2^2 square feet.
The total walkway area is thus x^2 + 4(2^2) + 4(x*2).
We want to find the dimensions of the garden. To do this, we need to find the value of x.
Let's sum up the garden dimensions and the walkway dimensions:
x^2 + 4(2^2) + 4(x*2) = 196 sq ft
x^2 + 16 + 8x = 196 sq ft
x^2 + 8x - 180 = 0
(x-10(x+18) = 0
x=10 or x=-18. We must discard x=-18, since the side length can't be negative. We are left with x = 10 feet.
The garden dimensions are (10 feet)^2, or 100 square feet.