Question

Triangle fgh is an isosceles right triangle with a hypotenuse that measures 16 units. an altitude, line segment g j, is drawn from the right angle to the hypotenuse. what is the length of line segment g j? 2 units 4 units 6 units 8 units

Answer 1

The square of the altitude is equal to the product of the base of the triangles

Triangular altitude theorem

The square of the altitude is equal to the product of the base of the triangles. The length of line segment GJ is 8units

According to the theorem;

GJ² = HJ*JF

Determine the value of x using the pythagorean theorem

$x^2+x^2=16\\2x^2=16\\x^2=8\\x=\sqrt{8}\\x=2\sqrt{2}$

According to the theorem;

GJ² = HJ*JF

HJ + JF = 16

Since HJ = JF, hence

HJ = JF = 8

Substitute

GJ² = HJ*JF

GJ² = 8 * 8
GJ² = 64

GJ = 8units

Hence the length of line segment GJ is 8units

Learn more on triangular altitude theorem here: brainly.com/question/14357999?source=archive

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Answer 2

Answer:

8

Step-by-step explanation: