SOLUTION: Story Problem The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures square root symbol 6m. find the width and height. Textbook

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Question 32003: Story Problem
The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures square root symbol 6m. find the width and height.


Textbook Elementary and Intermediate Algebra. Mark Dugopolski
ISBN: 13978-0-07-326862-0
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length be x
let the width be x+2
THis makes it a pythagorean theorem question:
Equation:
x%5E2%2B%28x%2B2%29%5E2=6%5E2
x%5E2%2Bx%5E2%2B4x%2B4=36
2x%5E2%2B4x-32=0
x%5E2%2B2x-16=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=2, c=-16
x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A-16+%29%29%2F%282%2A1%29+
x=%28-2%2B-sqrt%284%2B64%29%29%2F2
Simplfy and remove the negative:
x=3.12
3.12+2=5.12
Hence, the width is 5.12 and the length is 3.12
Paul.