Question

A 2.6 m long rod leans against a wall, its foot 1 meters from the wall. When the foot is moved a little away from the wall, its upper end slides the same length down. How much farther is the foot moved?

Answer 1

Let the distance of the upper end of rod from ground be $x$.

The rod forms a right-angle triangle with the wall and ground.

So, using hypotenuse theorem:
${2.6}^2=1^2+x^2$
$\Rightarrow 6.76=1+x^2$
$\Rightarrow 5.76=x^2$
$\Rightarrow x=2.4$

Given that upper end moves down the same distance as the lower end moves away.

Let the rod move $y$ meters.

Using the hypotenuse theorem,
$(2.4-y{)}^2+(1+y{)}^2={2.6}^2$
$\Rightarrow 5.76-4.8y+y^2+1+2y+y^2=6.76$
$\Rightarrow 2y^2-2.8y+6.76=6.76$
$\Rightarrow 2y^2-2.8y=0$
$\Rightarrow 2y(y-1.4)=0$
$\Rightarrow y=0$ or $y=1.4$

But $y$ can’t be equal to 0.
So, the foot of the rod moved 1.4 m further.