Question

A diagram of a rectangular pool with a diagonal of 50 meters is shown below. Connected to the pool is a square shaped kid’s pool.What is the area of the kid’s pool in the diagram? Ulysses says the area of the kid’s pool is 900 square meters.Ursula says the area of the kid’s pool is 120 square meters. Which student is correct?

Answer 1

Let's find the length of the side of the pool.

Let it be x, so the diagram is:

Using the pythagorean theorem, we can figure out x. Shown below:

$\begin{gathered} x^2+40^2=50^2 \\ x^2=50^2-40^2 \\ x^2=900 \\ x=\sqrt[]{900} \\ x=30 \end{gathered}$

So, 30 meters is the side length of the square (pool).

The area of a square is:

$A=s^2$

Where "s" is the side length

We found s to be 30, thus the area of the pool is:

$\begin{gathered} A=s^2 \\ A=(30)^2 \\ A=900 \end{gathered}$

Thus,

Ulysses is correct.