Question

PLEASE HELP I NEEEEEEED IT ASAP

Answer 1

`x = √(6)`

`y=√(15)`

Explanation:

To find the value of x, apply the Geometric Mean Theorem (Altitude Rule).

The Geometric Mean Theorem (Altitude Rule) states that 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.

From inspection of the given right triangle:

• Altitude = x
• Segment 1 = 3
• Segment 2 = 2

`\implies \sf (altitude)/(segment\:1)=(segment\:2)/(altitude)`

`\implies (x)/(3)=(2)/(x)`

`\implies x^2=6`

`\implies x=√(6)`

Therefore, the value of x is √6.

To find the value of y, apply the Geometric Mean Theorem (Leg Rule).

The Geometric Mean Theorem (Leg Rule) states that the altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment segment directly opposite the leg.

From inspection of the given right triangle:

• Hypotenuse = 3 + 2 = 5
• Leg 1 = y
• Segment 1 = 3

`\implies \sf (hypotenuse)/(leg\:1)=(leg\:1)/(segment\;1)`

`\implies (5)/(y)=(y)/(3)`

`\implies y^2=15`

`\implies y=√(15)`

Therefore, the value of y is √(15).

Answer 2

• x = √6;
• y = √15.

------------------------

Apply geometric mean theorem to find the value of x:

• x² = 2*3
• x² = 6
• x = √6

Find the value of y using Pythagorean:

• y² = 3² + 6
• y² = 9 + 6
• y² = 15
• y = √15