Applying the leg rule, and solving algebraically, the lengths are determined as:
JG = 9
HJ = 12
<h3>What is the Leg Rule?</h3>
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:
brainly.com/question/25016594
