Question

Find the length of line segment KL.

Answer 1

Answer:

$8\sqrt{2}$

Step-by-step explanation:

Given:

A right angled triangle with:

length of hypotenuse = 12

length of base = 4

By pythagoras theorem we know that:

$(hypotenuse)^{2}=(base)^{2}+(altitude)^{2}$

$12^{2}=4^{2}+(KL)^{2}$

$KL=\sqrt{144-16}$

$KL=\sqrt{128}$

$KL=8\sqrt{2}$

Answer 2

Answer:

$\displaystyle 8\sqrt{2} = KL$

Step-by-step explanation:

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

$\displaystyle a^2 + b^2 = c^2 \\ \\ -4^2 + 12^2 = b^2 → -16 + 144 = b^2 → \sqrt{128} = \sqrt{b^2} \\ \\ 8\sqrt{2} = b$

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