SOLUTION: The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures square root of 6m. Find the width and height. Iam having a problem solving with

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Question 209795: The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures square root of 6m. Find the width and height. Iam having a problem solving with that m under the square root sign.
Answer by Theo(3464) About Me  (Show Source):
You can put this solution on YOUR website!
diagonal is sqrt%286m%29
in a right triangle, hypotenuse squared = width squared plus length squared.
in this rectangle, width = h + 2
in this rectangle, length = height = h
the diagonal of the gate is the hypotenuse of a right triangle.
your formula is:
w%5E2+%2B+h%5E2+=+d%5E2
where:
w is the width of the gate
h is the height of the gate
d is the diagonal of the gate.
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since you know that d = sqrt%286%29, then d^2 must be equal to 6 meters because sqrt%286%29%5E2+=+6
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since you know that w = h+2, then you can substitute h+2 for w.
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your formula becomes:
%28h%2B2%29%5E2+%2B+h%5E2+=+6
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since:
%28h%2B2%29%5E2+=+h%5E2+%2B+4h+%2B+4
your formula becomes:
h%5E2+%2B+4h+%2B+4+%2B+h%5E2+=+6
combine like terms to get:
2h%5E2+%2B+4h+%2B+4+=+6
subtract 6 from both sides of the equation to get:
2h%5E2+%2B+4h+-+2+=+0
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solve using the quadratic formula to get:
h = .414213562 meters.
this makes:
w = 2.414213562 meters.
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this checks out because h%5E2+%2B+w%5E2+=+sqrt%286%29%5E2
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quadratic formula is:
h+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29
the equation you are placing into this formula is:
2h%5E2+%2B+4h+-+2
the factors you will be using are:
a = 2
b = 4
c = -2
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you replace the a in the formula with 2.
you replace the b in the formula with 4.
you replace the c in the formula with -2.
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then you solve.
you will get one positive answer and one negative answer. the negative answer is no good because h = height can't be negative. only the positive answer is good. that value should be the value i calculated for you.
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