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

no

step-by-step explanation:

2-7=-5

7-2=5

when you combing like terms for ech expression, 5 and -5. these numbers are not equal to each other.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.