A 13-ft ladder is leaning against a house. The distance from the bottom of the ladder to the house is 7-ft less than the distance from the top of the ladder to the ground. How far is the bottom of the ladder from the house?

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