SOLUTION: A lumber mill cuts rectangular beams from circular logs. If diameter of the log is 16 inches and the cross-sectional area of the beam is 120 square inches.find the dimensions of th

Algebra ->  Formulas -> SOLUTION: A lumber mill cuts rectangular beams from circular logs. If diameter of the log is 16 inches and the cross-sectional area of the beam is 120 square inches.find the dimensions of th      Log On


   

Question 1115568: A lumber mill cuts rectangular beams from circular logs. If diameter of the log is 16 inches and the cross-sectional area of the beam is 120 square inches.find the dimensions of the cross section of the beam correct to the one decimal place.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A lumber mill cuts rectangular beams from circular logs.
If diameter of the log is 16 inches and the cross-sectional area of the beam is 120 square inches.
find the dimensions of the cross section of the beam correct to the one decimal place.
:
A rectangular beam from a circular log is a square.
The diameter of the log is the hypotenuse of the cross section of the square beam
:
let L = one side of the cross section of the beam,
let w = the other side
:
L*w = 120
L = 120/w
:
using Pythagoras:
L^2 + w^2 = 16^2
L^2 = 256 - w^2
L = sqrt%28256-w%5E2%29
plot these two equations
+graph%28+300%2C+200%2C+-3%2C+18%2C+-3%2C+18%2C+120%2Fx%2C+sqrt%28256-x%5E2%29%29+
points of intersection
9.1355287, 13.1355287 and 13.1355287, 9.1355287
correct to one decimal point. cross section
length = 13.1 inches; width 9.1 inches