Question

10. In right triangle FGH shown below,
mZGHF-90, altitude HJ is drawn to FG,
FJ = 16, and HG = 15.[Only algebraic solutions
can receive full credit.]

Determine and state length of JG

Determine and state length of HJ

Answer 1

Applying the leg rule, and solving algebraically, the lengths are determined as:

JG = 9

HJ = 12

What is the Leg Rule?

The Leg rule states that when an altitude bisects the right angle of a right triangle and intersects the hypotenuse, then, hypotenuse/leg = leg/part.

Find length of JG using algebraic solutions and the leg rule:

Let JG = x

Hypotenuse = x + 16

Leg = 15

Part = x

Therefore:

(x + 16)/15 = 15/x (leg rule)

Cross multiply

x(x + 16) = (15)(15)

x² + 16x = 225

x² + 16x - 225 = 0

Factorize

(x + 25)(x − 9) = 0

x = -25 or x = 9

The length of JG (x) cannot be negative, therefore, the length of JG = 9.

Find length of JG using algebraic solutions:

Let HJ = y

Based on the altitude theorem, we would have:

y = √(16 × JG)

Substitute

y = √(16 × 9)

y = √(144)
y = 12

Therefore, the length of HJ is: 12.

Learn more about the leg rule on:

https://brainly.com/question/25016594