Hello,
I have solve the ans, you can read this
Let's analyze the problem step by step:
The hypotenuse of a right triangle is equal to one of its legs: $AB = AC$.
The area of square $BCDE$ is given as $144$. Since the square has sides equal to the legs of the right triangle, its area is also equal to the product of the legs: $AB \cdot AC = 144$.
We are asked to find integer values of $AB$ and $AC$ that are each less than $20$.
Now, we can find the possible integer pairs of $(AB, AC)$ that satisfy the conditions.
Since $AB = AC$, we have $AB^2 = 144$, which implies $AB = \sqrt{144} = 12$.
Therefore, there is only one possibility for the lengths of $AB$ and $AC$, which is $AB = AC = 12$.
So, there is only one possibility for the lengths of $AB$ and $AC$ that satisfies the given conditions.
I hope my ans. is good.
