Answer:
12 feet
Step-by-step explanation:
As a ladder is leaning against a house, it forms right angle triangle. And for right angleΔ, we use Pythagoras theorem.i.e
P²+B²= H²
Where,
'P' is perpendicular i.e the distance from the top of the ladder to the ground
'B' is base i.e be the distance from the bottom of the ladder to the house
'H' is hypotenuse i.e 13
considering 'x' as perpendicular
So, base would be 'x-7'
Applying Pythagoras theorem,
x² + (x-7)²= 13²
x² +x² -14x +49 =169
2x² -14x -120= 0
x² -7x -60=0 ----> solving the quadratic equation
x² + 5x -12x-60=0
x(x+5) -12(x+5)=0
Either : x+5=0 => x=-5
OR: x-12=0 => x=12
We'll choose the positive length.
therefore , The distance from the bottom of the ladder to the house is 12 feet
