2W + 15 - 15 = 0 - 15...............&...............W - 6 + 6 = 0 + 6
2W = - 15...............&................W = 6
...................note: W cannot be negative because it would result to a negative measurement,
............................so let's just drop the left equation.
W = 6 feet
░░░░░░░░
......................substitute this to the equation for L;
L = 3 + 2W
...= 3 + ( 2 • 6 )
...= 3 + 12
...= 15 feet
░░░░░░░░
# 24 )))
let's presume that this is a right triangle with one side horizontal and the other side is vertical:
area of triangle = ½ A • B = 110 ft ²
½ A • B = 110
½ ( 2x + 2 ) • ( x ) = 110
½ ( 2x ² + 2x ) = 110
x ² + x = 110
.....................subtract 110 from both sides of the equation;
x ² + x - 110 = 110 - 110
x ² + x - 110 = 0
....................factor the expression on the left;
( x + 11 ) ( x - 10 ) = 0
................................= (x)(x) + (x)(-10) + (11)(x) + (11)(-10)
................................= x ² - 10x + 11x - 110
................................= x ² + x - 110
....................now, either of the terms in the parenthesis could be equated to zero;
x + 11 = 0...............&...............x - 10 = 0
....................subtract 11 from both sides of the left equation, &
....................add 10 to both sides of the right equation;
x + 11 - 11 = 0 - 11...............&...............x - 10 + 10 = 0 + 10
x = - 11...............&...............x = 10
...................note: x cannot be negative because it would result to a negative measurement,
............................so let's just drop the left equation.
x = 10 ft.
░░░░░░