Answer that goes in the box = 28
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Step-by-step explanation:
We have a white triangle shown as the empty space between the green squares.
This right triangle has the following sides:
- a = unknown horizontal leg
- b = 6 = vertical leg
- c = 8 = hypotenuse
Use the Pythagorean Theorem to solve for 'a'
a^2 + b^2 = c^2
a^2 + 6^2 = 8^2
a^2 + 36 = 64
a^2 = 64 - 36 ..... subtract 36 from both sides
a^2 = 28
a = sqrt(28) .... apply the square root to both sides
Optionally we can simplify like so
a = sqrt(28)
a = sqrt(4*7)
a = sqrt(4)*sqrt(7)
a = 2*sqrt(7)
But this would not fit the answer format your teacher has provided. So we'll stick to sqrt(28) as the final answer.