A rectangle is inscribed in a right triangle with legs of length 3 and 4. Express the area A of the rectangle as a function of x.

What is x ?

That's all the problem says

There must be a diagram with it or something to tell you what x is

If x is the height of the rectangle, with base along the leg of length 4, then

A = 4/3 x(3-x)

To solve this problem, let's start by drawing a diagram of the right triangle and the inscribed rectangle.

First, draw a right triangle with legs of length 3 and 4. Then, draw a rectangle inside the triangle so that two vertices of the rectangle lie on the legs of the triangle. Let's denote the length of the rectangle as x.

/|
/ |
/ |
x/ |
/ |
3 /_____|/______ 4

Without loss of generality, let's assume that the length of the rectangle is along the side of length 4. Then, the width of the rectangle will be along the side of length 3.

The area of a rectangle is given by the formula A = length × width. In this case, the length of the rectangle is x, and the width is 3.

Therefore, the area of the rectangle is A = x × 3, or simply A = 3x.

So, the area of the rectangle, A, can be expressed as a function of x: A(x) = 3x.