SOLUTION: The length of a bulletin board is 1 foot more than the width. The diagonal has a length of sqrt3feet (ft). Find the length and width of the bulletin board.

Click here to see ALL problems on Square-cubic-other-roots

Question 313271: The length of a bulletin board is 1 foot more
than the width. The diagonal has a length of sqrt3feet (ft).
Find the length and width of the bulletin board.
Found 2 solutions by mananth, unlockmath:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
let the width be x feet
the length will be x+1 feet
the diagonal is sqrt 3
..
They form a right angle
..
sqrt3 ^2 = x^2+(x+1)^2
3=x^2+x^2+2x+1
2x^2+2x-2 =0
x^2+x-1=0
..
find the roots of the equation .
x1= (-1 + (sqrt1+4)) /2
x1=0.61
x2=(-1 - (sqrt1+4)) /2
x2= -1.61
width = 0.61 feet
Length will be 1+0.62 = 1.61 feet.

Answer by unlockmath(1688) (Show Source):
You can put this solution on YOUR website!
Hello,
Let the width be x and the length be x+1. Now we can use the Pythagorean formula:
a^2+b^2=c^2 Plug in what we have:
x^2+(x+1)^2= (sq rt3)^2 This can be rewritten as:
2x^2+2x+1=3 Subtract 3 from both sides to get:
2x^2+2x-2=0 From here we need to use the quadratic formula:
Plug in the numbers:
x = -2 +- sqrt( 4+16)/(4) So we come up with 2 answers for x being:
x=.62 (approx)
x=-6.47 (approx) The negative doesn't make sense in our problem so .62 is the length of one side and 1.62 is the length of the other.
Make sense?
RJ www.math-unlock.com