Answer:
x = 5
which agrees with the first answer option listed
Explanation:
Use the proportionality associated with similar triangles, considering that the larger triangle has sides:
x + (x+5) = 2 x + 5
and
(x+1) + (x-2) = 2 x - 1
and the smaller triangle:
x and (x-2)
The we build the following proportionality:
(2 x + 5) / x = (2 x - 1) / (x - 2)
cross multiply to eliminate denominators:
(2 x + 5) (x - 2) = x (2 x - 1)
operate:
2 x^2 - 4 x + 5 x -10 = 2 x^2 - x
combine like terms:
2 x^2 + x -10 = 2 x^2 - x
subtract 2 x^2 from both sides:
x - 10 = - x
add x to both sides:
2 x -10 = 0
add 10 to both sides
2 x= 10
divide both sides by 2:
x = 5
which agrees with the first answer option listed