Question

PLEASE HELP ALL INFO IN THE IMAGE PLS ANSWER ASAP SHOW WORK

Answer 1

x = 14

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Apply geometric mean theorem:

• the geometric mean of the two segments equals the altitude, or

• (x + 14)² = x*56

Solve for x:

• (x + 14)² = x*56
• x² + 28x + 196 = 56x
• x² - 28x + 196 = 0
• (x - 14)² = 0
• x - 14 = 0
• x = 14

Answer 2

x = 14

Explanation:

Geometric Mean Theorem - Altitude Rule

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude.

`\boxed{\sf (altitude)/(segment\:1)=(segment\:2)/(altitude)}`

From inspection of the given right triangle:

• Altitude = (x + 14)
• Segment 1 = x
• Segment 2 = 56

To find the value of x, substitute the values into the formula and solve for x:

`\implies ((x+14))/(x)=(56)/((x+14))`

`\implies (x+14)(x+14)=56x`

`\implies x^2+28x+196=56x`

`\implies x^2-28x+196=0`

`\implies x^2-14x-14x+196=0`

`\implies x(x-14)-14(x-14)=0`

`\implies (x-14)^2=0`

`\implies x-14=0`

`\implies x=14`

Therefore, the value of x is 14.