Write each of the relations below in algebra and see if it gives a polynomial. Give reasons for your conclusion also.
An 1 metre wide path goes around a square ground. The relation between the length of a side of the ground and the area of the path.

Question

Write each of the relations below in algebra and see if it gives a polynomial. Give reasons for your conclusion also.
Two poles of heights 3 metres and 4 metres are erected upright on the ground, 5 metres apart. A rope is to be stretched from the top of one pole to some point on the ground and from there to the top of the other pole:

The relation between the distance of the point on the ground from the foot of a pole and the total length of the rope.

Philoid · Accepted Answer

Let the distance of the point on ground be x m from the 3 m pole.

⇒ This distance of the point on ground from 4 m pole is (5-x) m. (∵ the distance between the poles is 5 m.)

Now the length of the rope is AB + BC.

By Pythagoras Theorem

AB² = AD² + DB²

⇒ AB² = 3² + x²

⇒

Similarly,

Now, let the length of rope be a R

⇒ R = AB + BC

⇒