Thread: Optimization Problem

Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 4 cm if two sides of the rectangle lie along the legs.

I drew a picture and i know I'm trying to maximize the area so i need to use the area formula, but I'm not really sure where to start, not sure how the 4 and 3 cm are related to the rectangle other than the fact it cannot have length or widths greater than those.

Any help would be greatly appreciated

Let one leg of the triangle lie on the x-axis, and the other leg lie on the yaxis. Let the vertex of the rectangle that touches the hypotenuse be (x,y). What is the area of the rectangle, and how can you relate x and y?

yeah, the area would be xy but im not sure how it relates to the 3cm and 4cm

Can you state the linear function along which the hypotenuse lies? This will depend upon which of the legs is horizontal and which is vertical.