Please solve asap I don’t know how do this question

Mathematics

1 answer:

soldier1979 [14.2K]3 years ago

6 0

Answer:

x = 9

Step-by-step explanation:

All of the right triangles in the figure are similar. That means ratios of corresponding sides are the same.

The two sides marked with numerical values have lengths 5 and 2√5 ≈ 4.47. The remainder of x, which is (x-5), will be shorter than either of the other two marked lengths. This means we can write the ratio of short side to long side of the two smaller triangles as ...

short side / long side = (2√5)/5 = (x-5)/(2√5)

Cross-multiplying gives ...

20 = 5(x -5)

4 = x -5 . . . . . divide by 5

9 = x . . . . . . . add 5

_____

<em>Additional comment</em>

In this geometry, as we have seen above, the square of the altitude ((2√5)²=20) is the product of the lengths of the segments of the hypotenuse (5×4=20). There are two other "geometric mean" relationships in a triangle like this, involving the legs of the largest triangle. They all arise from the similarity of the triangles.

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First, to find the simplest form of a fraction, you'll need to find the greatest common factor (GCF). To do this, we can list the factors of 2 and 4 and find the first common one.

Factors of 2: 1, 2
Factors of 4: 1, 2, 4

Since 2 is our first common factor, it is our GCF.

Second, we can now take our GCF (2) and divide it with our numerator and denominator. We will get a new numerator and denominator.

$2 \div 2 = 1 \\ 4 \div 2 = 2$

Answer in fraction form: $\fbox {1/2}$
Answer in decimal form: $\fbox {0.5}$