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3 years ago

What is the value of x?

Mathematics

2 answers:

borishaifa [10]3 years ago

5 0

Answer:

I believe it is x+3..

Step-by-step explanation:

Anton [14]3 years ago

3 0

Answer:

x = 5

which agrees with the first answer option listed

Step-by-step 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

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