Question

Find the length of line segment KL.

Answer 1

`\displaystyle 8√(2) = KL`

Step-by-step explanation:

Since the hypotenuse is already defined, we use the Pythagorean Theorem in reverse, using Subtraction:

`\displaystyle a^2 + b^2 = c^2 \\ \\ -4^2 + 12^2 = b^2 → -16 + 144 = b^2 → √(128) = √(b^2) \\ \\ 8√(2) = b`

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Answer 2

`8√(2)`

Explanation:

Given:

A right angled triangle with:

length of hypotenuse = 12

length of base = 4

By pythagoras theorem we know that:

`(hypotenuse)^(2)=(base)^(2)+(altitude)^(2)`

`12^(2)=4^(2)+(KL)^(2)`

`KL=√(144-16)`

`KL=√(128)`

`KL=8√(2)`