SOLUTION: the width of a rectagular gate is 2 meters larger than its height. The diagonal brace measures the square root of 6 meters. Find the width and height.

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Question 142587This question is from textbook University of Phoenix Elementary and Intermediate Algebra
: the width of a rectagular gate is 2 meters larger than its height. The diagonal brace measures the square root of 6 meters. Find the width and height. This question is from textbook University of Phoenix Elementary and Intermediate Algebra

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
let width be w.
let height be h
Given w+=+h+%2B+2
Given diagonal = sqrt(6)
Pythagorean theorem states c%5E2+=+a%5E2+%2B+b%5E2
(diagonal is c, a and b are width and height)
6+=+w%5E2+%2B+h%5E2
6+=+%28h%2B2%29%5E2+%2B+h%5E2
6+=+h%5E2+%2B+4h+%2B+4+%2B+h%5E2
0+=+2h%5E2+%2B+4h+-+2
0+=+h%5E2+%2B+2h+-1
Use quadratic equation and solve. a = 1, b=2, c =(-1)
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+