Question

A ladder that is 13 meters long is leaning against a wall. The distance between the foot of the ladder and the wall is 7 meters less than the distance between the top of the ladder and the ground. Create an equation that models the length of the ladder in terms of x, which is the distance between the top of the ladder and the ground.

Answer 1

oh no :DDDD
so you gan take the pythagorean formula, as it is a right triangle and modify dat.

`169 = {x}^(2) + {(x - 7)}^(2)`
twelve and five if yuo need to know numbres :DDDD

Answer 2

The equation that is used to model the length of ladder in terms of x is:

`x^2-7x-60=0`

Explanation:

We can model this problem with the help of a right angled triangle whose hypotenuse is 13 meters and the other two legs are x meters and (x-7) meters.

where x is the distance between the top of the ladder and the ground.

and (x-7) is the distance between the foot of the ladder and the wall.

Hence, using Pythagorean Theorem we have:

`13^2=x^2+(x-7)^2\\\\i.e.\\\\169=x^2+x^2+49-14x\\\\i.e.\\\\169=2x^2-14x+49\\\\i.e.\\\\2x^2-14x+49-169=0\\\\i.e.\\\\2x^2-14x-120=0\\\\i.e.\\\\x^2-7x-60=0`

Hence, the answer is:

`x^2-7x-60=0`