SOLUTION: Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, than what are the lengths of the sides?

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Question 148820This question is from textbook Elementary and Intermediate Algebra
: Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, than what are the lengths of the sides?This question is from textbook Elementary and Intermediate Algebra

Answer by jim_thompson5910(28717) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=length of one side and y=length of other side

Since "One side of a rectangular stage is 2 meters longer than the other", this means that y=x%2B2 (note: the order does not matter). Also, since the "diagonal is 10 meters", we can use Pythagoreans Theorem to get

x%5E2%2By%5E2=10%5E2 which becomes x%5E2%2By%5E2=100


x%5E2%2By%5E2=100 Start with the second equation.


x%5E2%2B%28x%2B2%29%5E2=100 Plug in y=x%2B2


x%5E2%2Bx%5E2%2B4x%2B4=100 Foil.


x%5E2%2Bx%5E2%2B4x%2B4-100=0 Get all terms to the left side.


2x%5E2%2B4x-96=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=4, and c=-96


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%282%29%28-96%29+%29%29%2F%282%282%29%29 Plug in a=2, b=4, and c=-96


x+=+%28-4+%2B-+sqrt%28+16-4%282%29%28-96%29+%29%29%2F%282%282%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16--768+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-96%29 to get -768


x+=+%28-4+%2B-+sqrt%28+16%2B768+%29%29%2F%282%282%29%29 Rewrite sqrt%2816--768%29 as sqrt%2816%2B768%29


x+=+%28-4+%2B-+sqrt%28+784+%29%29%2F%282%282%29%29 Add 16 to 768 to get 784


x+=+%28-4+%2B-+sqrt%28+784+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-4+%2B-+28%29%2F%284%29 Take the square root of 784 to get 28.


x+=+%28-4+%2B+28%29%2F%284%29 or x+=+%28-4+-+28%29%2F%284%29 Break up the expression.


x+=+%2824%29%2F%284%29 or x+=++%28-32%29%2F%284%29 Combine like terms.


x+=+6 or x+=+-8 Simplify.


So the possible answers are x+=+6 or x+=+-8


However, since a negative length is not possible, this means that the only answer is x+=+6

y=x%2B2 Go back to the first equation.


y=6%2B2 Plug in x+=+6.


y=8 Add.


So the dimensions of the rectangle are 6 and 8