SOLUTION: The width of a rectangular gate is 2 meters(m) larger than its height. The diagonal brace measures the square root of 6. find the width and height.

Algebra ->  Volume -> SOLUTION: The width of a rectangular gate is 2 meters(m) larger than its height. The diagonal brace measures the square root of 6. find the width and height.      Log On


   



Question 118067: The width of a rectangular gate is 2 meters(m) larger than its height. The diagonal brace measures the square root of 6. find the width and height.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the pythagorean formula
c%5E2+=+a%5E2+%2B+b%5E2
where c is the diagonal, a is the width, b is the height
%28sqrt%286%29%29%5E2+=+%28x+%2B+2%29%5E2+%2B+x%5E2
6+=+x%5E2+%2B+4x+%2B+4+%2B+x%5E2
2x%5E2+%2B+4x+-+2+=+0
x%5E2+%2B+2x+-+1+=+0
x%5E2+%2B+2x++=+1
Complete the square. Take 1/2 of the coefficient of the x term
square it, and add it to both sides
x%5E2+%2B+2x+%2B+1+=+2
%28x+%2B+1%29%5E2+=+2
x+%2B+1+=+0+%2B-+sqrt%282%29
x+=+-1+%2B-+sqrt%282%29
x+=+-1+%2B+sqrt%282%29 The other solution is negative,
so it must be rejected
The width is x+%2B+2, so
width = 2+-+1+%2B+sqrt%282%29
width = 1+%2B+sqrt%282%29 answer
Height = x
height = -1+%2B+sqrt%282%29 answer
check
%28sqrt%286%29%29%5E2+=+%28x+%2B+2%29%5E2+%2B+x%5E2
%28sqrt%286%29%29%5E2+=+%28-1+%2B+sqrt%282%29+%2B+2%29%5E2+%2B+%28-1+%2B+sqrt%282%29%29%5E2
6+=+1+%2B+2%2Asqrt%282%29+%2B+2+%2B+1+-+2%2Asqrt%282%29+%2B+2
6+=+6
OK