the width of a rectangular gate = 2m < than its height the diagonal brace meas. sq root of 6m find the w and h

Answer 1

damn easy man. w=.4142m and h=2.4142m

use pythagoras theorem and solve the quadratic eq

Answer 2

Let height = x m
Width = x - 2 m
x² + (x - 2)² = 6
x² + x² - 4x + 4 = 6
2x² - 4x - 2 = 0
x² - 2x - 1 = 0
x = [ 2 ± √8 ] / 2
x = [2 ± 2.√2] / 2
x = 1 ± √2
x = 2.414 (taking +ve value of square root)
Height = 2.414 m
Width = 0.414 m

Answer 3

w=h-2

(h-2)^2 + h^2 =6
h^2 -4h +4 +h^2 = 6
2h^2 -4h -2 =0

h= (4+/-sqrt(16+16))/4
h= (4 +sqrt(32))/4 (negative root is meaningless here)
h=2.414 meters