The length that can be cut off from the three given pieces of wood equally to form a right triangle is 5 cm
Given parameters:
dimension of the three pieces of wood = 20 cm, 41 cm and 44 cm
To find:
let the length that is cut off from each of the wood = y
From Pythagoras theorem, we will have the following equation.
[tex](44-y)^2 = (20-y)^2 + (41-y)^2\\\\expand \ the \ equation \ as \ follows;\\\\1936 - 88y + y^2 = 400 - 40y + y^2 + 1681 - 82y + y^2\\\\simplify \ by \ collecting \ similar \ terms \ together\\\\(1936 - 400- 1681) + (-88y + 40y+ 82y) + (y^2 - 2y^2) = 0\\\\-145 +34y - y^2 = 0\\\\multiply \ through \ by \ (-1)\\\\y^2-34y + 145 = 0\\\\factorize \ the \ above \ quadratic\ equation\\\\y^2 -5y - 29y + 145 = 0\\\\y(y - 5) -29(y - 5)=0 \\\\(y -5)(y-29) = 0\\\\y = 5 \ \ \ or \ \ \ \ y = 29[/tex]
Since the least measurement of one of the pieces of the wood is 20 cm, we cannot cut off 29 cm.
Thus, the highest amount we can cut off equally is 5 cm
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