Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 4 cm and 5 cm if two sides of the rectangle lie along the legs.

Step-by-step explanation:

We need to maximize the area of the rectangle inside the triangle, in this case, it is:

the length of this rectangle is (4-x) and width is y.

No, we need to represent y in terms of x. We can use this ratio property here:

Let's solve it for y:

Then the area will be:

Now, let's take the derivative of A whit respect to x.

And equal to zero to get the maximum value of x and solve it for x.

Therefore, the area of largest rectangle will be

I hope it helps you!