SOLUTION: The width of a rectangle gate is 2 meters larger than its height. The diagonal breace measures (sqrt 6 meters). Find the width and the height.
I'm lost. I think I need to set
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Question 207744This question is from textbook Elementary and Intermediate Algebra
: The width of a rectangle gate is 2 meters larger than its height. The diagonal breace measures (sqrt 6 meters). Find the width and the height.
I'm lost. I think I need to set it up as a^2 + b^2 = c^2, I'm not sure...but I still don't know where to go from there. Please help!!
This question is from textbook Elementary and Intermediate Algebra
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The width of a rectangle gate is 2 meters larger than its height. The diagonal breace measures (sqrt 6 meters). Find the width and the height.
.
You need to apply Pythagorean theorem:
Let h = height
then
h+2 = width
.
h^2 + (h+2)^2 = 6^2
h^2 + (h+2)(h+2) = 36
h^2 + (h^2+4h+4) = 36
2h^2+4h+4 = 36
h^2+2h+2 = 18
h^2+2h-16 = 0
(h+8)(h-2) = 0
h = {-8,2}
We can toss out the negative solution leaving:
h = 2 meters (height)
.
h+2 = 2+2 = 3 meters (width)
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