SOLUTION: Matt is building a new barn, with length 10 yards more than the width. While determining the footprint of the barn, he measured the diagonal as 50 yards. What will be the dimension

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Matt is building a new barn, with length 10 yards more than the width. While determining the footprint of the barn, he measured the diagonal as 50 yards. What will be the dimension      Log On


   

Question 1130466: Matt is building a new barn, with length 10 yards more than the width. While determining the footprint of the barn, he measured the diagonal as 50 yards. What will be the dimensions of the barn?
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer.  Dimensions are 30 yards by 40 yards.


Classic  (3,4,5)-right angled triangle.


Algebra solution 

x^2 + (x+10)^2 = 50^2

x^2 + x^2 + 20x + 100 = 2500

2x^2 + 20x + (100-2500) = 0

2x^2 + 20x - 2400 = 0

x^2 + 10x - 1200 = 0

(x-30)*(x+40) = 0


The only positive root  x= 30  is meaninful, leading to the answer.

Solved.