Answer:
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To find the length of the beam that supports the wall, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two beams are perpendicular to each other, forming a right triangle. Let's label the length of the beam we want to find as "c" and the lengths of the other two beams as "a" and "b".
Using the Pythagorean theorem:
c^2 = a^2 + b^2
Substituting the given values:
c^2 = 4^2 + 2^2
c^2 = 16 + 4
c^2 = 20
To find the length "c", we take the square root of both sides:
c = √20 ≈ 4.5 meters (rounded to one decimal place)
Therefore, the length of the beam that supports the wall is approximately 4.5 meters.
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