Question

Y
3
Solve for x.
X
N
7
x = [?]

Answer 1

Answer:

x ≈ 4.6

Step-by-step explanation:

To find the altitude x , we can use the Geometric mean theorem.

The ratio of one segment to the altitude is equal to the ratio of the altitude to the other segment.

$\frac{altitude}{segment1}$ = $\frac{segment2}{altitude}$

Then

$\frac{x}{3}$ = $\frac{7}{x}$ ( cross multiply )

x² = 3 × 7 = 21 ( take square root of both sides )

$\sqrt{x^2}$ = $\sqrt{21}$ , that is

x = $\sqrt{21}$ ≈ 4.6 ( to the nearest tenth )

Answer 2

Answer:

x = 4.6

Step-by-step explanation:

In the given right triangle, the altitude is drawn from the right angle to the hypotenuse, separating the hypotenuse into two segments.

According to the Geometric Mean Theorem (Altitude Rule), the ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude:

$\boxed{\sf \dfrac{Altitude}{Segment\:1}=\dfrac{Segment\:2}{Altitude}}$

In this case, the altitude is x, and the two segments measure 3 and 7 units, respectively. Therefore:

$\dfrac{x}{3}=\dfrac{7}{x}$

Solve for x by cross-multiplying:

$x\cdot x=7 \cdot 3\\\\x^2=21$

Now, square root both sides:

$\sqrt{x^2}=\sqrt{21}\\\\x=\sqrt{21}\\\\x=4.58257569...\\\\x=4.6\; \sf (nearest\;tenth)$

Therefore, the value of x is:

$\LARGE\boxed{\boxed{x=4.6}}$