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?

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) (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 (note: the order does not matter). Also, since the "diagonal is 10 meters", we can use Pythagoreans Theorem to get

which becomes

Start with the second equation.

Plug in

Foil.

Get all terms to the left side.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, since a negative length is not possible, this means that the only answer is

Go back to the first equation.

Plug in .

Add.

So the dimensions of the rectangle are 6 and 8
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