Question

Find the value of y please ASAP

Answer 1

x/3 = 12/x

x^2 = 36

x = 6

9/y = y /x

9/y = y / 12

y^2 = 9 * 12

y = 9 * 4 * 3

y = 6√3

Answer

y = 6√3

Answer 2

Right Triangle Altitude Theorem

Draw the altitude of a right triangle from the vertex of the right angle to the hypotenuse, then:

Part a: the measure of the altitude is the geometric mean between the measures of the two segments of the hypotenuse.

Part b: each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.

Using Part b,

$\dfrac{12}{y} = \dfrac{y}{9}$

$y^2 = 12 \times 9$

$y = \sqrt{9 \times 4 \times 3}$

$y = 3 \times 2 \times \sqrt{3}$

$y = 6\sqrt{3}$

Answer: $~~~6\sqrt{3}$