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

Dec 23, 2016

6 metres and 8 metres

#### Explanation:

Let the length of 1 side be $x$
Then the length of the other is $x + 2$

The diagonal is given as 10 metres long

So we have a triangle. Using Pythagoras:

${x}^{2} + {\left(x + 2\right)}^{2} = {10}^{2}$

$2 {x}^{2} + 4 x + 4 = 100$

Divide through out by 2

${x}^{2} + 2 x + 2 = 50$

${x}^{2} + 2 x - 48 = 0$

$\left(x - 6\right) \left(x + 8\right) = 0$

$x = 6 \text{ and } x = - 8$ are solutions

It is not logical to have a negative value as a length of the rectangle

So the sides are of length $\text{ "6" metres & "6+2=8" metres}$