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(35256) 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