Answer:
Leg1 = 9 and leg2 = 12
Step-by-step explanation:
Points to remember
Pythagorean theorem
Hypotenuse² = Base² + Height²
To find the length of each leg
It is given that, hypotenuse = 15 feet
Let base = x the height = x +3
By using Pythagorean theorem we can write,
Hypotenuse² = Base² + Height²
15² = x² + (x + 3)²
225 = x² + x² + 6x + 9
2x² + 6x + 216 = 0
x² + 3x + 108 = 0
By solving we get x = 9 and x -12
Therefore one leg = 9 and other leg = 9 + 3 = 12
Answer:
One leg = x = 9.
Other leg = x+3 = 9+3 = 12.
Step-by-step explanation:
We have given hypotenuse = 15 feet and one leg is more than other the other of a right triangle.
We need to find the each leg of the right triangle.
Let the one leg = x.
Let the other leg = x+3.
We know that, Pythagoras theorem:
[tex]Hypotenuse^{2} = Perpendicular^{2} + Base^{2}[/tex]
Hypotenuse = 15, one leg(base) = x and other leg(perpendicular) = x+3.
By applying pythagoras theorem:
[tex]15^{2} = x^{2} + ( x+3)^{2}[/tex]
225 = x^{2} + x^{2} + 9 +6x
225 = 2x^{2} + 6x + 9
Subtracting 9 from both sides
216 = 2x^{2} + 6x
2x^{2} + 6x -216 = 0
Taking 2 common,
x^{2} + 3x - 108 = 0
x^{2} + 12x - 9x - 108 = 0
x(x+12) - 9(x+12) = 0
(x+12) (x-9)
x = -12, x = 9.
So, we will consider positive value x = 9.
Therefore, one leg = x = 9.
Other leg = x+3 = 9+3 = 12.
