Question 148013
Hi, Hope I can help
.
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?
.
First you will need to draw a rectangle, with a line in the middle, going from one corner to the other
.
We can look and see that it makes two triangles, they are both right triangles.
.
We can use the Pythagorean theorem,
.
{{{ a^2+b^2=c^2 }}}
.
The shorter side is "x", the longer side is two more than the shorter,or (x + 2)
.
We can replace "a" and "b" in the Pythagorean theorem, "a" and "b" are the sides
, "c" is the hypotenuse, or diagonal
.
{{{ (x+2)^2+x^2=10^2 }}}
.
{{{ (x+2)^2+x^2=100 }}}
.
We can now solve it even more
.
{{{ (x^2 + 4x +4)+x^2=100 }}}
.
{{{ x^2 + 4x +4+x^2=100 }}}
.
{{{ 2x^2 + 4x +4=100 }}}
.
We can divide everything by "2"
.
{{{ (2x^2 + 4x +4)/2=100/2 }}}
.
{{{ x^2 + 2x +2=50 }}}
.
We will move the 50 over to the left side
.
{{{ x^2 + 2x +2-50=50-50 }}}
.
{{{ x^2 + 2x -48=0 }}}
.
We can factor this quadratic equation to {{{ (x+8)(x-6) = 0 }}}( (-6) + 8 = 2 )
.
We can now solve for "x", taking one factor at a time
.
{{{ (x+8) = 0 }}}
{{{ x+8 = 0 }}}
{{{ x+8 - 8 = 0 - 8 }}}
{{{ x = -8 }}}
.
The next factor
.
{{{ (x-6) = 0 }}}
{{{ x-6 = 0 }}}
{{{ x-6 + 6 = 0 + 6 }}}
{{{ x = 6 }}}
.
x can be either (-8), or 6
.
Our "x" is = 6 meters ( measurements can't be negative)
The shorter side was "x" or 6 meters, our longer side is (x+2) or 8 meters
.
You can check by replacing "a" and "b" in the Pythagorean theorem
.
{{{ a^2+b^2=c^2 }}}
.
{{{ 8^2+6^2=10^2 }}}
.
{{{ 64+36=100 }}}
.
{{{ 100=100 }}}
.
Shorter Side = 6 meters
Longer Side = 8 meters
.
Hope I helped, Levi