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

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Question 150354This question is from textbook
: Diagonal brace. The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures√6m. Find the width and height.
This question is from textbook

Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!
In a rectangle, the one side is always longer than the other.
We mark "x"= height.
And the other side is 2m longer than this, so "x+2m"=the longer side (accdg. to your problem is the width).
Since we have a brace of sqrt%286%29, go by Pyth. Theorem to solve the other sides.
%28sqrt%286%29%29%5E2=x%5E2%2B%28x%2B2%29%5E2
6=x%5E2%2Bx%5E2%2B4x%2B4 -----------> 2x%5E2%2B4x-2=0----> x%5E2%2B2x-1=0
By quadratic,
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A-1=8.

Discriminant d=8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+8+%29%29%2F2%5C1+=+0.414213562373095
x%5B2%5D+=+%28-%282%29-sqrt%28+8+%29%29%2F2%5C1+=+-2.41421356237309

Quadratic expression 1x%5E2%2B2x%2B-1 can be factored:
1x%5E2%2B2x%2B-1+=+1%28x-0.414213562373095%29%2A%28x--2.41421356237309%29
Again, the answer is: 0.414213562373095, -2.41421356237309. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-1+%29

Use x=0.414m
To check,
%28sqrt%286%29%29%5E2=0.414%5E2%2B%282%2B0.414%29%5E2
6=0.17%2B5.83
6m=6m
Thank you,
Jojo